SOLUTION: Find the sum of infinite series 2/5+6/25+10/125+14/625 ...

Question 1116634: Find the sum of infinite series 2/5+6/25+10/125+14/625
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Answer by ikleyn(52779) (Show Source): You can put this solution on YOUR website!
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S         = 2/5 + 6/25 + 10/125 + 14/625 + . . . 

S/5       =       2/25 +  6/125 + 10/625 + . . .     Take the difference

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S - (S/5) = 2/5 + 4/25 + 4/125  + 4/625 + . . . =


          = 2/5 + 4*(1/25 + 1/125 + 1/625 + . . . )


          =  +  =  +  =  =   ====>


 =   ====>  S =  =  = 0.75.


Answer.  2/5 + 6/25 + 10/125 + 14/625 + . . .  =  = 0.75.


Check.   2/5 + 6/25 + 10/125 + 14/625          =      0.7424.

Solved.

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