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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 .
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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.
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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.   NB: You may find the following ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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Find the sum of the first three terms of $ \sum_{r=1}^{n}\left(3 r^{2}+r-2\right)$
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Find the sum of the first three terms of $ \sum_{r=1}^{n}\left(3 r^{2}+r-2\right)$\begin{aligned} &\text { Find the sum of the first three terms of } \sum_{r=1}^{n}\left(3 r^{2}+r-2\right) \text {. } \end{aligned} ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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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
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The rational function $\frac{x^{5}+1}{\left(x^{2}-1\right)^{2}}$ has a partial fraction expansion of the form
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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- ...
by MathsGee Platinum
(103,164 points)
asked in Mathematics Jan 13
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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
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What is the series expansion of the natural logarithm?
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What is the series expansion of the natural logarithm?What is the series expansion of the natural logarithm? ...
by MathsGee Platinum
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asked in Mathematics Jan 11
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What is a coefficient?
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The binomial coefficient is defined as ...
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The binomial coefficient is defined as ...The binomial coefficient is defined as ... ...
by Pieter SIlver Status
(18,261 points)
asked in Data Science & Statistics Dec 16, 2021
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Find the first three terms, in ascending powers of \(x\), of the binomial expansion \((1-2 x)^{5}\)
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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 ...
by MathsGee Platinum
(103,164 points)
asked in Mathematics Nov 9, 2021
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Expand \((1+4 x)^{8}\) in ascending powers of \(x\), up to and including \(x^{3}\), simplifying each coefficient in the expansion.
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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.
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Given that the first two terms, in ascending powers of \(x\), in the series expansion of \(\mathrm{f}(x)\) are 384 and \(-104 x\)
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Find the first 3 terms in ascending powers of \(x\) of the binomial expansion of \(\left(2+\frac{x}{2}\right)^{6}\)
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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 ...
by MathsGee Platinum
(103,164 points)
asked in Mathematics Nov 9, 2021
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Use the binomial theorem to expand
1 answer 278 views
Use the binomial theorem to expandUse binomial theorem $$ \begin{aligned} (a+b)^{n} &=\left(\begin{array}{c} n \\ 0 \end{array}\right) a^{n}+\left(\begin{array}{c} n \\ 1 \end{arra ...
by Pieter SIlver Status
(18,261 points)
asked in Mathematics May 10, 2021
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Can you determine the general $a_{n} ?$
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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 ...
by MathsGee Platinum
(103,164 points)
asked in Mathematics May 9, 2021
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During expansion, the spaces between the particles get........ , and during contraction, the spaces between the particles get........ .
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Expand $\left(x^{1/2} - 2y^{1/3}\right)^4$ using the binomial theorem
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Expand $\left(x^2+\dfrac{y}{2}\right)^3$ using the binomial theorem
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Expand $(3x+y)^5$ using the binomial theorem
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Expand $(3x+y)^5$ using the binomial theoremExpand $(3x+y)^5$ using the binomial theorem ...
by MathsGee Platinum
(103,164 points)
asked in Mathematics May 11, 2020
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Find the first three terms in the binomial expansion of $(8-3x)^{\frac{1}{3}}$. Simplify each term.
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Find the first four terms in the binomial expansion $(1-y^{-1})^{17}$. Simplify each term
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