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Series: - e ^x = 1 + x + (x^2)/ 2! + (x^3)/3! + …..

Here! is factorial notation.

This series expansion helps to evaluate the complex problems in a very easy manner. Only thing here is to remember the general expansion of the exponential series. This tool guides to solve problems where complex exponential function involves, and without solving this one cannot even think to solve such complicated problems. The above important points can be more clarified by the following examples:-

Series: - e ^x = 1 + x + (x^2)/ 2! + (x^3)/3! + …..

Now by substituting x = 1 in above equation

Therefore e^1 = 1+ 1 + (1^2)/2! + (1^3)/3! +…

So e ^1 is approximately equals to 2.67

Series: - e ^x = 1 + x + (x^2)/ 2! + (x^3)/3! + …..

This implies, e ^2 = 1 + 2 + (4)/ 2 + (8)/3*2+ …..

Now by substituting x = 2 in above equation

Therefore e^1 = 1+ 2 + (2^2)/2! + (2^3)/3! +…

So e ^1 is approximately equals to 7.3