Use the formula for the sum of a geometric series to find the sum. sum_{n=4}^infty(-frac49)^n

foass77W 2020-10-20 Answered
Use the formula for the sum of a geometric series to find the sum.
n=4(49)n
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Expert Answer

Pohanginah
Answered 2020-10-21 Author has 96 answers
Given series:
n=4(49)n
For the given series the ratio of (n+1)-th term to n-th term is constant which is 49
Hence, the terms of the given series are in geometric progression.
Write the given series in standard geometric series form.
That is,
n=4(49)n=(49)4+(49)3+(49)2+(49)1+n=0(49)n
n=4(49)n=4365256+n=0(49)n
The general geometric series,
n=0arn, where a is the first term and r is the common ratio
converges to a1r, for -1<r<1
Otherwise it diverges.
Compare the series n=0(49)n with the general geometric series, to get
a=1,r=49(1,1)
Hence, n=0(49)n=11(49)
=11+49
=1(139)
=913
Plug n=0(49)n=913 in equation (1), to get
n=4(49)n=4365256+913
=590493328
17.7431
Thus,
n=4(49)n=17.7431
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Jeffrey Jordon
Answered 2021-12-27 Author has 2047 answers

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