Which of the following best describes the terms of the series- 1-2 n C 1-2 n -3 C 2-3 n -4 C 3- - -1 n -11- n -1 n C nA- -1r-1r-rr-1n CrB- -1rr-r-1-rn CrC- -1r-1r-r-1n Cr-1D- -1r-1r-1-r-n Cr

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Proof by mathematical induction

Which of the ...

Question

Which of the following best describes the terms of the series? $\frac{1}{2}$ $^{n} C_{1}$ - $\frac{2}{3}$ $^{n} C_{2}$ + $\frac{3}{4}$ $^{n} C_{3}$ ................... $(- 1)^{n + 1}$ $\frac{1}{n + 1}$ $^{n} C_{n}$

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(\begin{matrix} n + 1 r + 1 \end{matrix}) : (\begin{matrix} n r \end{matrix}) : (\begin{matrix} n - 1 r - 1 \end{matrix}) = 11 : 6 : 3,,

n

r

lim x \to \infty \frac{1 \cdot n \sum r = 1 r + 2 \cdot n - 1 \sum r = 1 r + 3 \cdot n - 2 \sum r = 1 r + . . . . + n \cdot 1}{n^{4}}

n \sum r = 1 (- 1)^{r - 1} .^{n} C_{r} (a - r)

Find the value of $n \sum r = 1 (- 1)^{r + 1}$ $^{n - 1} C_{r - 1}$

\sum_{r = 1}^{n} (r^{2} + 1) r!

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