Prove that 7n 1 - n7 - nn-17-14 - nn-1n-27-14-21 - - - 4n 1 - n2 - nn-12-4 - nn-1n-22-4-6 - -

RHS=4^n[1 12]^ n #160; #160; #160; #160; #160; #160; =8^n where n is positive amp; LHS=7^n[1+17]^n =7^n[87]^n =8^n ...

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Summation by Sigma Method

Prove that ...

Question

Prove that
$7^{n} {1 + \frac{n}{7} + \frac{n (n - 1)}{7.14} + \frac{n (n - 1) (n - 2)}{7.14.21} + . . . .}$
$= 4^{n} {1 + \frac{n}{2} + \frac{n (n - 1)}{2.4} + \frac{n (n - 1) (n - 2)}{2.4.6} + . . . .}$

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