C 1-c0-2 - c 2-n-1-3 - c 2- c 2- n - c n-n1- -n-1-2- nn-1-2- nn-1-n-1D- nn-2-2

The correct option is A G.R=n/1+2n(n 1)/2/n+3n(n 1)(n 2)/3!/n(n 1)/2+……+n1/n=n+(n 1)+(n 2)+……+2+1 =1+2+3+……+… +n=n(n+1)/2 ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

c 1/c0+2 · c ...

Question

$\frac{c_{1}}{c_{0}} + 2. \frac{c_{2}}{c_{1}} + 3. \frac{c_{3}}{c_{2}} + . . . + n . \frac{c_{n}}{n_{1}}$ =

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Solution

The correct option is A
G.R= $\frac{n}{1} + 2 \frac{\frac{n (n - 1)}{2}}{n} + 3 \frac{\frac{\frac{n (n - 1) (n - 2)}{3!}}{n (n - 1)}}{2} + \dots \dots + n \frac{1}{n} = n + (n - 1) + (n - 2) + \dots \dots + 2 + 1 = 1 + 2 + 3 + \dots \dots + \dots + n = \frac{n (n + 1)}{2}$

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Similar questions

Q. Value of

S = \frac{1}{m!} C_{0} + \frac{n}{(m + 1)!} C_{1} + \frac{n (n - 1)}{(m + 2)!} C_{2} + . . . . . + \frac{n (n - 1) . . .2 .1}{(m + n)!}

If $(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + . . . . . . . + C_{n} x^{n}$ , then $\frac{C_{1}}{C_{0}} + \frac{2 C_{2}}{C_{1}} + \frac{3 C_{3}}{C_{2}} + . . . . . . . . + \frac{n C_{n}}{C_{n - 1}} =$

If $(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + . . . . . . . + C_{n} x^{n}$ , then

$\frac{C_{1}}{C_{0}}$ + $\frac{2 C_{2}}{C_{1}}$ + $\frac{3 C_{3}}{C_{2}}$ + ........+ $\frac{n C_{n}}{C_{n - 1}}$ =

Q. The sum to (n + 1) terms of the series

\frac{c_{0}}{2} - \frac{c_{1}}{3} + \frac{c_{2}}{4} - \frac{c_{3}}{5} + . . . . i s

Q. Assertion :

\frac{1}{m!} C_{0} + \frac{n}{(m + 1)!} C_{1} + \frac{n (n - 1)}{(m + 2)!} C_{2} + . . . . . + \frac{n (n - 1) . . .2 .1}{(m + n)!} C_{n} = \frac{(m + n + 1) (m + n + 2) . . . (m + 2 n)}{(m + n)!}

Reason: for

r \geq 0

(\begin{matrix} m r \end{matrix}) C_{0} + (\begin{matrix} m r - 1 \end{matrix}) C_{1} + . . . . . . (\begin{matrix} m 0 \end{matrix}) C_{r} = (\begin{matrix} m + n r \end{matrix})

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c1c0+2.c2c1+3.c3c2+...+n.cnn1=

The correct option is A G.R=n1+2n(n−1)2n+3n(n−1)(n−2)3!n(n−1)2+……+n1n=n+(n−1)+(n−2)+……+2+1=1+2+3+……+…+n=n(n+1)2

$\frac{c_{1}}{c_{0}} + 2. \frac{c_{2}}{c_{1}} + 3. \frac{c_{3}}{c_{2}} + . . . + n . \frac{c_{n}}{n_{1}}$ =

The correct option is A
G.R= $\frac{n}{1} + 2 \frac{\frac{n (n - 1)}{2}}{n} + 3 \frac{\frac{\frac{n (n - 1) (n - 2)}{3!}}{n (n - 1)}}{2} + \dots \dots + n \frac{1}{n} = n + (n - 1) + (n - 2) + \dots \dots + 2 + 1 = 1 + 2 + 3 + \dots \dots + \dots + n = \frac{n (n + 1)}{2}$