We were asked to evaluate the following series: <munderover> &#x2211;<!-- ∑ --> <mrow cl

nileteenice

nileteenice

Answered question

2022-05-22

We were asked to evaluate the following series:
n = 2 7 5 n 2 3 n 2

Answer & Explanation

Kaiden Porter

Kaiden Porter

Beginner2022-05-23Added 10 answers

Assuming you have ( 5 ) n upstairs in the sum.
Try to write the terms of this Geometric series in standard form:
7 ( 5 ) n 2 3 n 2 = 7 ( 5 ) n 2 2 2 3 n = 4 7 ( 5 ) n ( 2 3 ) n = 28 ( 5 8 ) n .
Then n = 2 7 ( 5 ) n 2 3 n 2 = n = 2 28 ( 5 8 ) n = 28 ( 5 / 8 ) 2 1 ( 5 / 8 ) = 28 25 / 64 13 / 8 = 28 25 13 8 = 25 7 13 2 .
(The sum of a convergent Geometric series is the first term divided by (1- ratio)).

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