# In series 1+2+4+....find the ratio between sum of the 5 terms and sum of the square of the same 5 terms.

1
by deeenbe

2015-04-05T01:04:26+05:30

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Sum of terms = 1 + 2 + 4 + 8 + 16 = 31

sum of squares of terms = 1 + 4 + 16 + 64 + 256 = 341

ratio =  31 / 341 = 1 / 11

as it is only 5 terms, i do that directly , without any algebraic formulas.
sorry,it is correct.
sum of terms Sn is a Geometric progression with a = 1, and r = 2. So Sn = 1 (2^n - 1)/(2-1) = 2^n - 1.
sum of squares of the terms Rn is a geometric series with a = 1 , r = 4. So Rn = 1 (4^n - 1)/(4-1) = (2^n - 1)(2^n + 1) / 3
The ratio = Sn / Rn = 3/(2^n + 1). Hence, S5 / R5 = 3/33 = 1/11
this is the algebraic way of solving the above .