If S1,S2,....Sn are the sums of n terms of n G.P.'s whose first term i

1.	If S1,S2,....Sn are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ...., n respectively, then prove that. S1+S2+2S3+3S4+....(n−1) Sn=1n+2n+3n+...+nn.
Answer» If $S_{1}, S_{2}, . . . . S_{n}$ are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ...., n respectively, then prove that. $S_{1} + S_{2} + 2 S_{3} + 3 S_{4} + . . . . (n - 1)$ $S_{n} = 1^{n} + 2^{n} + 3^{n} + . . . + n^{n}$ .

If S1,S2,....Sn are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ...., n respectively, then prove that. S1+S2+2S3+3S4+....(n−1) Sn=1n+2n+3n+...+nn.

Answer»

If $S_{1}, S_{2}, . . . . S_{n}$ are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ...., n respectively, then prove that. $S_{1} + S_{2} + 2 S_{3} + 3 S_{4} + . . . . (n - 1)$

$S_{n} = 1^{n} + 2^{n} + 3^{n} + . . . + n^{n}$ .

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If S1,S2,....Sn are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ...., n respectively, then prove that. S1+S2+2S3+3S4+....(n−1) Sn=1n+2n+3n+...+nn.

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