Infinite Sum

Number Theory Level pending

+ 0.0366 + 0.11 + 0.333 + 1 + 0.5 + 0.25 + 0.125 + = ? \dots+0.0366+0.11+0.333+1+0.5+0.25+0.125+\dots = ?

9.924 4.992 3.259 2.499

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1 solution

Zeeshan Ali
Feb 9, 2015

... ... ... + 0.0366 + 0.11 + 0.333 + 1 + 0.5 + 0.25 + 0.125 + ... ... ...
The given series is the combination of two converging geometric series as below;
1 . ... ... ... + 0.0366 + 0.11 + 0.333
2. 1 + 0.5 + 0.25 + 0.125 + ... ... ...
and the general formula for summation is as under:
S = a1 / (1 - r) where r = a2/a1
therefore sum to infinity of first series is 1 / (1 - 0.5) = 2 and the sum of second series is 0.499 and sum of combination is then 2.499

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