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Find the sum of each of the following in...

Find the sum of each of the following infinite series :
`2/5+3/5^(2)+2/5^(3)+3/5^(4)+...oo`

Text Solution

Verified by Experts

The correct Answer is:
`13/24`
`S=(2/5+2/5^(3)+2/5^(5)+...oo)+(3/5^(2)+3/5^(4)+3/5^(6)+...oo)`
`=a_(1)/((1-r_(1)))+a_(2)/((1-r_(2)))`, where `(a_(1)=2/5, r_(1)=1/25) and (a_(2)=3/25, r_(2)=1/25)`
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