If 1-xn-C0-C1 x- -Cn xn- then the value of -r-0n-s-0n Cr Cs is equal to

∑_r=0^n∑_s=0^n C_r C_s=∑_r=0^n(C_r∑_s=0^n C_s)=(∑_r=0^n C_r)(∑_s=0^n C_s) =2^n· 2^n=2^2 n ...

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Sum of Coefficients of All Terms

If 1+xn=C0+C1...

Question

If $(1 + x)^{n} = C_{0} + C_{1} x + \dots + C_{n} x^{n},$ then the value of $n \sum r = 0 n \sum s = 0 C_{r} C_{s}$ is equal to

2^{n}

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2^{2 n}

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2^{n + 1}

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2^{3 n}

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Solution

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Similar questions

{(1 + x)}^{n} = n \sum r = 0^{n} C_{r}

(\frac{C_{0} + C_{1}}{C_{0}}) (\frac{C_{1} + C_{2}}{C_{1}}) (\frac{C_{2} + C_{3}}{C_{2}}) . . . . . . . . . (\frac{C_{n - 1} + C_{n}}{C_{n - 1}})

{(1 + x)}^{n} = \sum_{r = 0}^{n} C_{r} x^{r}

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

C_{0} . C_{1}, C_{2}, . . ., C_{n}

(1 + x)^{n}

n \sum 0 \frac{C_{k}}{k + 1}

{(1 + x)}^{n} = C_{0} + C_{1} x + . . . + C_{n} x^{n}

\sum 0 \leq r < \sum s \leq n (C_{r} + C_{s})

(1 + x)^{n} = n \sum r = 0 = C_{r} x^{r}

\frac{C_{1}}{C_{0}} + \frac{2 C_{2}}{C_{1}} + \frac{3 C_{8}}{C_{2}} + . . . + \frac{n C_{n}}{C_{n - 1}} = \frac{1}{k} n (n + 1)

k

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