Saturday 20 December 2014

Computing to infinity



How much is
1/7 +2/7² + 1/7⁴ + 1/7⁵+ 2/7⁶ + 1/7⁷ ……. To infinity?

Answer:    We must, first of all separate the sum into two parts, x and y.
X = 1/7 + 1/7ᶾ + 1/7⁵ + ……… 1/ 7²n-1
Y = 2/7² + 2/7⁴ + 2/ 7⁶ ….. 2/ 7²n
X = 1/7 /1- 7² = 7/48
Y = 2/7² / 1-1/7² = 2/48
7/48   + 2/48 = 9/48 = 3/16

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