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

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Question 1116634: Find the sum of infinite series 2/5+6/25+10/125+14/625
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Answer by ikleyn(52778) About Me  (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 + . . . )


          = 2%2F5 + 4%2A%28%28%281%2F25%29%29%2F%281-1%2F5%29%29 = 2%2F5 + %284%2A5%29%2F%2825%2A4%29 = 2%2F5+%2B+1%2F5 = 3%2F5  ====>


%284%2F5%29%2AS = 3%2F5  ====>  S = %28%283%2F5%29%29%2F%28%284%2F5%29%29 = 3%2F4 = 0.75.


Answer.  2/5 + 6/25 + 10/125 + 14/625 + . . .  = 3%2F4 = 0.75.


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

Solved.