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Maclaurin Series for e^x

Taylor series of the exponential at 0.

Formula

e^x = \sum_{n=0}^{\infty}\frac{x^n}{n!}

xVariable

nTerm index

e^1 = 1 + 1 + 1/2 + 1/6 + 1/24 + … ≈ 2.718.

Setting x=1 in the series for e^x gives the famous sum 1 + 1 + 1/2 + 1/6 + ··· = e.