Value of -k-1-kr-013kkCr is-

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Value of ∑∞...

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Value of $\infty \sum k = 1 k \sum r = 0 \frac{1}{3^{k}} (^{k} C_{r})$ is?

\frac{2}{3}

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\frac{4}{3}

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\infty \sum k = 1 k \sum r = 0 \frac{1}{3^{k}} (^{k} C_{r})

\infty \sum k = 1 k \sum r = 0 \frac{1}{3^{k}} (^{k} C_{r}) =

r = 3

k r^{2} - k r - 3 = 0

k

4 \times 0 + 1 = 01

4 \times 1 + 2 = 06

4 \times 2 + 3 = 11

4 \times 3 + 4 = 16

4 \times 8 + 9

S_{n} = n \sum k = 1 \frac{k}{(k - 1)^{4 / 3} + (k^{2} - 1)^{2 / 3} + (k + 1)^{4 / 3}}

lim n \to \infty \frac{S_{n}}{n^{2 / 3}} = \frac{1}{p} .

p

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