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How To Find the Sum of a Series
Infinite sum
sum_(k=0)^∞ x^k = 1/(1 - x) when abs(x)<1
Partial sum formula
sum_(k=0)^n x^k = (-1 + x^(1 + n))/(-1 + x)
Series representation
1/(1 - x) = sum_(n=0)^∞ x^n for abs(x)<1
1/(1 - x) = sum_(n=-∞)^∞ ( piecewise | -1 | n = -1 0 | otherwise) (-1 + x)^n