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Expert: - 12/2/2009


Question
infinite series
infinity symbol
n=1                  (1/4)^n=?


(1/4)^1+(1/4)^2+(1/4)^3+(1/4)^4+(1/4)^5+.....+(1/4)^n+.......and so on. show all work if possible.

Answer
For the sum(n=0 to infinity)(a^n), if |a|<1, it is 1/(1-a).
We have this with a = 1/4, missing the first term, term 0.
The sum including term 0 turns out to be 1/(1 - 1/4) = 1/(3/4) = 4/3.
Since term 0 is 1, the answer is 4/3 - 1 = 4/3 - 3/3 = 1/3.

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