Find the sum of the series. sum_(n=1)^(infty) 7/(4^n)

vangstosiis 2022-07-29 Answered
Find the sum of the series.
n = 1 7 4 n
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Answers (1)

kamphundg4
Answered 2022-07-30 Author has 20 answers
n = 1 = 7 ( 1 4 + ( 1 4 ) 2 + ( 1 4 ) 3 + . . . + ( 1 4 ) N + . . . )
= 7 4 ( 1 + ( 1 4 ) 2 + ( 1 4 ) 3 + . . . . ) this is a geometric series
r = 1 4 < 1
and
1 + r 2 + r 3 + r 4 + . . . . . . . . . . . + r n 1 = lim n 1 r n 1 r = 1 1 r   i f   | r | < 1
lim n 7 4 ( 1 ( 1 4 ) n 1 1 4 ) = lim n 7 4 1 3 4 = 7.4 4.3 = 7 3
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