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The sum of infinity of the series 7/5²+10/5³+.............is please solve fully

The sum of infinity of the series 7/5²+10/5³+.............is please solve fully

Grade:11

1 Answers

Arun
25750 Points
5 years ago
S∞ = 7/5² + 10/5³ + .............................
S∞/5 =         7/5³ + .......................
-              -    -        -
S∞(1-1/5) = 7/5² + 3/5³ + .............
4S∞/5 =  7/ 52+ 3/5( 1/5² + .........................................)
4S∞/5 = 7/ 5^2 + 3/5(1/5^2/(1-1/5))
4S∞/5 = 7/25 + (3/5)(1/20)
4S∞/5 = 31/100
S∞ = 31/400
 
 

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