∑_n=1^10[∏_k=1^nk+1k] =∑_n=1^10[21×32×43×...×n+1n] =∑_n=1^10[n+1] =2+3+4+...+11 =65 ...

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Multinomial Expansion

∑n=110[∏k=1nk...

Question

$10 \sum n = 1 [n \prod k = 1 \frac{k + 1}{k}] =$

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Solution

$10 \sum n = 1 [n \prod k = 1 \frac{k + 1}{k}]$

$= 10 \sum n = 1 [\frac{2}{1} \times \frac{3}{2} \times \frac{4}{3} \times . . . \times \frac{n + 1}{n}]$

$= 10 \sum n = 1 [n + 1]$

$= 2 + 3 + 4 + . . . + 11$

$= 65$

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