Mathematics: Find the sum of this infinite geometric series: 4 - 2.88 + 2.0736- 1.492992+

Find the sum of this infinite geometric series: 4

Ответ:

haileyrae187

07.01.2022

Mathematics

Let

be the common ratio between terms. Then

$-2.88=4r\implies r=-0.72$

Now denote the

th partial sum of the series by

$S_n=4-2.88+2.0736-1.492992+\cdots+4(-0.72)^{n-1}+4(-0.72)^n$

Multiply both sides by -0.72

, then subtract from the above to get

$S_n-(-0.72S_n)=4-4(-0.72)^{n+1}$
$1.72S_n=4(1-(-0.72)^{n+1})$
$S_n=2.32558(1-(-0.72)^{n+1})$

As $n\to\infty$ , you're left with

$S_\infty=2.32558$

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Ответ:

curtisepps

07.04.2020

Mathematics

ok then why did you put points

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Find the sum of this infinite geometric series: 4 - 2.88 + 2.0736- 1.492992+

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