Find the sum of the infinite geometric series. sum_{i=1}^infty12(-0.7)^{i-1}

CoormaBak9 2021-02-09 Answered
Find the sum of the infinite geometric series.
i=112(0.7)i1
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Expert Answer

toroztatG
Answered 2021-02-10 Author has 98 answers

To find:
The sum of the infinite series i=112(0.7)i1
Concept used:
The sum of infinite geometric series can be obtained by the formula,
S=a1r(r<1)
Here, a is first term, r is common ratio and S is sum of infinite geometric series.
Calculation:
Expand the summation as follows:
i=112(0.7)i1=12(0.7)11+12(0.7)21+12(0.7)31+...
=12+12(0.7)+12(0.7)2+...
It is observed from the series that the first term is 12 and common ratio is (−0.7) and common ratio is less than 1.
Substitute 12 for a and (−0.7) for r in equation (1).
S=1210(0.7)
=121+0.7
=121.7
=7.06
Thus, the sum of the infinite series is 7.06.

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Jeffrey Jordon
Answered 2021-12-27 Author has 2047 answers

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