3 votes

What is the procedure to find the sum of the series

** How could the procedure used to ** ** be the sum of the series? **
 $$ \ begin {align} & 1. \ qquad \ sum_ {n = 1} ^ {\ infty} {2 {^ {2n +1}} \ over 5 ^ n} \ end {align} $$ `

3voto

Anon User Points 0
`
 $$ \ begin {align} & S = 2 \ sum_ {n = 1} ^ {\ infty} \ left (\ dfrac {4} {5} \ right) ^ n \\ & \\ & \ text {as 4 / 5 <1 then the series converges} \\ & \\ & S = 2 \ cdot \ dfrac {4/5} {1-4 / 5} \\ & \\ & s = 8 \ end {align} $$ `That's all.

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