Evaluating series <munderover> &#x2211;<!-- ∑ --> <mrow class="MJX-TeXAtom-ORD"> n

Hector Petersen

Hector Petersen

Answered question

2022-06-15

Evaluating series n = 1 n 2 ( 1.05 ) n

Answer & Explanation

Abigail Palmer

Abigail Palmer

Beginner2022-06-16Added 30 answers

Let
f ( x ) = n = 1 n 2 x n , | x | < 1
and then
0 x f ( t ) t d t = n = 1 n x n = x ( 1 x ) 2 .
So
f ( x ) = x ( x ( 1 x ) 2 ) = .
So
n = 1 n 2 ( 1.05 ) n = f ( 1 1.05 ) = .

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