# Recent questions tagged expansion

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Find the value of $\mathrm{k}$ if the constant term in the expansion $\left(\mathrm{k} x-\frac{1}{x^{2}}\right)^{6}$ is 240 .
Find the value of $\mathrm{k}$ if the constant term in the expansion $\left(\mathrm{k} x-\frac{1}{x^{2}}\right)^{6}$ is 240 .Find the value of $\mathrm{k}$ if the constant term in the expansion $\left(\mathrm{k} x-\frac{1}{x^{2}}\right)^{6}$ is 240 . ...
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Find a formula in terms of $n$ for $\sum_{r=1}^{n}\left(3 r^{2}+r-2\right)$. Simplify your answer fully.
Find a formula in terms of $n$ for $\sum_{r=1}^{n}\left(3 r^{2}+r-2\right)$. Simplify your answer fully. Find a formula in terms of $n$ for $\sum_{r=1}^{n}\left(3 r^{2}+r-2\right)$. Simplify your answer fully. &nbsp; NB: You may find the following ...
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Find the sum of the first three terms of $\sum_{r=1}^{n}\left(3 r^{2}+r-2\right)$
Find the sum of the first three terms of $\sum_{r=1}^{n}\left(3 r^{2}+r-2\right)$\begin{aligned} &amp;\text { Find the sum of the first three terms of } \sum_{r=1}^{n}\left(3 r^{2}+r-2\right) \text {. } \end{aligned} ...
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Using the geometric series $\frac{1}{1-x}=1+x+x^{2}+x^{3}+\ldots$, it follows that $\frac{1}{1+x^{3}}$ has the power series expansion
Using the geometric series $\frac{1}{1-x}=1+x+x^{2}+x^{3}+\ldots$, it follows that $\frac{1}{1+x^{3}}$ has the power series expansionUsing the geometric series $\frac{1}{1-x}=1+x+x^{2}+x^{3}+\ldots$, it follows that $\frac{1}{1+x^{3}}$ has the power series expansion A. $\quad 1-x^{ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The rational function$\frac{x^{5}+1}{\left(x^{2}-1\right)^{2}}$has a partial fraction expansion of the form 0 answers 5 views The rational function$\frac{x^{5}+1}{\left(x^{2}-1\right)^{2}}$has a partial fraction expansion of the formThe rational function$\frac{x^{5}+1}{\left(x^{2}-1\right)^{2}}$has a partial fraction expansion of the form A.$\quad f(x)=G x^{2}+F x+\frac{A}{(x- ...
Using the geometric series $\frac{1}{1-x}=1+x+x^{2}+x^{3}+\ldots$, it follows that $\frac{1}{1+x^{3}}$ has the power series expansion
Using the geometric series $\frac{1}{1-x}=1+x+x^{2}+x^{3}+\ldots$, it follows that $\frac{1}{1+x^{3}}$ has the power series expansionUsing the geometric series $\frac{1}{1-x}=1+x+x^{2}+x^{3}+\ldots$, it follows that $\frac{1}{1+x^{3}}$ has the power series expansion A. $\quad 1+x^{ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the series expansion of the natural logarithm? 1 answer 6 views What is the series expansion of the natural logarithm?What is the series expansion of the natural logarithm? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is a coefficient? 1 answer 19 views What is a coefficient?What is a coefficient? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The binomial coefficient is defined as ... 1 answer 27 views The binomial coefficient is defined as ...The binomial coefficient is defined as ... ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the first three terms, in ascending powers of $x$, of the binomial expansion $(1-2 x)^{5}$ 1 answer 72 views Find the first three terms, in ascending powers of $x$, of the binomial expansion $(1-2 x)^{5}$(a) Find the first three terms, in ascending powers of $x$, of the binomial expansion $(1-2 x)^{5}$ (b) Find the first three terms, in ascending ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the first four terms, in ascending powers of $x$, of the binomial expansion $(2+k x)^{6}$ Given that the coefficient of the $x^{3}$ term in the expansion is $-20$ 1 answer 58 views Find the first four terms, in ascending powers of $x$, of the binomial expansion $(2+k x)^{6}$ Given that the coefficient of the $x^{3}$ term in the expansion is $-20$(a) Find the first four terms, in ascending powers of $x$, of the binomial expansion $(2+k x)^{6}$ Given that the coefficient of the $x^{3}$ ter ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Expand $(1+4 x)^{8}$ in ascending powers of $x$, up to and including $x^{3}$, simplifying each coefficient in the expansion. 1 answer 27 views Expand $(1+4 x)^{8}$ in ascending powers of $x$, up to and including $x^{3}$, simplifying each coefficient in the expansion.(a) Expand $(1+4 x)^{8}$ in ascending powers of $x$, up to and including $x^{3}$, simplifying each coefficient in the expansion. (b) Showing yo ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Using the last two terms of the binomial expansion, or otherwise, find the probability that Dave is late no more than one time in a school week. 1 answer 57 views Using the last two terms of the binomial expansion, or otherwise, find the probability that Dave is late no more than one time in a school week.(a) Fully expand $(p+q)^{5}$ The probability of Dave being late for school on any day is $0.1$. Let $\mathrm{p}$ represent the probability that ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Given that the first two terms, in ascending powers of $x$, in the series expansion of $\mathrm{f}(x)$ are 384 and $-104 x$ 1 answer 56 views Given that the first two terms, in ascending powers of $x$, in the series expansion of $\mathrm{f}(x)$ are 384 and $-104 x$(a) Find the first 3 terms in ascending powers of $x$ of the binomial expansion of $\left(2-\frac{x}{8}\right)^{7}$ $\mathrm{f}(x)=(a x+b)\left(2 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the first 3 terms in ascending powers of \(x$ of the binomial expansion of $\left(2+\frac{x}{2}\right)^{6}$ 1 answer 68 views Find the first 3 terms in ascending powers of $x$ of the binomial expansion of $\left(2+\frac{x}{2}\right)^{6}$(a) Find the first 3 terms in ascending powers of $x$ of the binomial expansion of $\left(2+\frac{x}{2}\right)^{6}$ (b) Use your expansion to fin ... close 1 answer 72 views close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Use the binomial theorem to expand 1 answer 278 views Use the binomial theorem to expandUse binomial theorem$\begin{aligned} (a+b)^{n} &amp;=\left(\begin{array}{c} n \\ 0 \end{array}\right) a^{n}+\left(\begin{array}{c} n \\ 1 \end{arra ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Can you determine the generala_{n} ?$0 answers 44 views Can you determine the general$a_{n} ?$Find a Taylor expansion for the solution$x(t)=a_{0}+a_{1} t+a_{2} t^{2}+\cdots$for the differential equation$\frac{d x}{d t}=t \cdot x$with the bo ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Tumi and Jason are helping their dad tile the bathroom floor. Their dad tells them to leave small gaps between the tiles. Why do they need to leave these small gaps? 1 answer 150 views Tumi and Jason are helping their dad tile the bathroom floor. Their dad tells them to leave small gaps between the tiles. Why do they need to leave these small gaps?Tumi and Jason are helping their dad tile the bathroom floor. Their dad tells them to leave small gaps between the tiles. Why do they need to leave th ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 During expansion, the spaces between the particles get........ , and during contraction, the spaces between the particles get........ . 1 answer 442 views During expansion, the spaces between the particles get........ , and during contraction, the spaces between the particles get........ .During expansion, the spaces between the particles get........ , and during contraction, the spaces between the particles get........ . ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Expand$\left(x^{1/2} - 2y^{1/3}\right)^4$using the binomial theorem 1 answer 212 views Expand$\left(x^{1/2} - 2y^{1/3}\right)^4$using the binomial theoremExpand$\left(x^{1/2} - 2y^{1/3}\right)^4$using the binomial theorem ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Expand$\left(x^2+\dfrac{y}{2}\right)^3$using the binomial theorem 1 answer 124 views Expand$\left(x^2+\dfrac{y}{2}\right)^3$using the binomial theoremExpand$\left(x^2+\dfrac{y}{2}\right)^3$using the binomial theorem ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Expand$(3x+y)^5$using the binomial theorem 1 answer 598 views Expand$(3x+y)^5$using the binomial theoremExpand$(3x+y)^5$using the binomial theorem ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the first three terms in the binomial expansion of$(8-3x)^{\frac{1}{3}}$. Simplify each term. 1 answer 916 views Find the first three terms in the binomial expansion of$(8-3x)^{\frac{1}{3}}$. Simplify each term.Find the first three terms in the binomial expansion of$(8-3x)^{\frac{1}{3}}$. Simplify each term. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the first four terms in the binomial expansion$(1-y^{-1})^{17}$. Simplify each term 1 answer 186 views Find the first four terms in the binomial expansion$(1-y^{-1})^{17}$. Simplify each termFind the first four terms in the binomial expansion$(1-y^{-1})^{17}\$. Simplify each term ...