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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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The function $f(x)=\frac{x^{3}-6 x}{x^{2}-4}$ is
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The function $f(x)=\frac{x^{3}-6 x}{x^{2}-4}$ isThe function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ is   A. even and has two vertical asymptotes, B. odd and has two vertical asymptotes, C. even ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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Find $\lim _{x \rightarrow 0}(1-\sin x)^{\frac{3}{x}}$
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Show that the series $\sum_{r=1}^{\infty}\left(\dfrac{1}{r+2}-\frac{2}{r+1}+\dfrac{1}{r}\right)$ converges and find its sum.
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Determine whether the following series converge or diverge. $\sum_{n=1}^{\infty} \dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}$
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Determine whether the following series converge or diverge. $\sum_{n=1}^{\infty}(-1)^{n}\left(\dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}\right)^{n}$

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Find partial fractions of $f(x)=\frac{4}{x^{3}-2 x^{2}-3 x}$
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Determine whether the series $\sum_{n \geq 1} \dfrac{1}{\sqrt{n^{3}}}$ converges or diverges. Give a reason for your answer. 

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Find the sum of the series $\sum_{n \geq 2} \frac{2}{n^{2}-1}$
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Prove that if the series $\sum_{n=1}^{\infty} a_{n}$ converges, then $\lim _{n \rightarrow \infty} a_{n}=0$
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Find the maxima and minima of $f(x)=\frac{x^{2}-3}{x+2}$
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Find the maxima and minima of $f(x)=\frac{x^{2}-3}{x+2}$Find the maxima and minima of $f(x)=\frac{x^{2}-3}{x+2}$ ...
by MathsGee Platinum
(103,792 points)
asked in Mathematics Jan 13
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Write $\frac{9-x^{2}}{x^{3}+9 x}$ in terms of its partial fractions.
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Decide (with reasons) if the following series converge or diverge. $\sum_{n=1}^{\infty}(-1)^{n} \frac{5-n+3 n^{2}}{7 n^{2}-19}$
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Determine if the following series converge $\sum_{n=1}^{\infty} 3^{3 n} 7^{2-n}$
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Determine if the following series converge $\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{2}}$
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Show that the series $ \sum_{n=2}^{\infty} \dfrac{2}{n(n+1)}$ converges and find its limit.
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Prove that if the series $\sum_{n=1}^{\infty} a_{n}$ converges, then $\lim _{n \rightarrow \infty} a_{n}=0$.
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Define the term relative standard deviation
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Define the term relative standard deviationDefine the term relative standard deviation ...
by MathsGee Platinum
(103,792 points)
asked in Data Science & Statistics Jan 12
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What does the term "unsaturated compounds" mean?
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What does the term "unsaturated compounds" mean?What does the term "unsaturated compounds" mean? ...
by Pieter SIlver Status
(18,309 points)
asked in Chemistry Jan 11
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What is meant by the term "homologous series"?
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What is meant by the term "homologous series"?What is meant by the term "homologous series"? ...
by Pieter SIlver Status
(18,309 points)
asked in Chemistry Jan 11
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What does the term "saturated compounds" mean?
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What does the term "saturated compounds" mean?What does the term "saturated compounds" mean? ...
by Pieter SIlver Status
(18,309 points)
asked in Chemistry Jan 11
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