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Sum of n terms of series 1/3+5/9+19/27+65/81.....is

Sum of n terms of series 1/3+5/9+19/27+65/81.....is

Grade:11

1 Answers

Aditya Gupta
2080 Points
3 years ago
kth term is (3^k – 2^k)/3^k
so, ak=1 – (2/3)^k
so, sum= ∑1 –  (2/3)^k
=n – 2/3*(1 – (2/3)^n)/(1 – 2/3)........[note that we are using sum of a gp formula here]
= n + 2*[(2/3)^n – 1]

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