Maclaurin Series formula

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What is Maclaurin Series

The Maclaurin series formula is a special case of the Taylor series formula. Or in other words, we can derive the Maclaurin formula from the Taylor series very easily.

Maclaurin series formula helps in writing a function as a series (or sum) of terms involving the derivatives of the function. This formula helps in finding the approximate value of the function.

e^x =1 + x + x²/2! + x³/3! + ……

How to find Maclaurin Series Formula

We can find or Derive the Maclaurin series from Taylor series.

Sol. As we Know Taylor series is:

Let f(x) = e^xand f(0)=1 (because we only know value of f at x0=1).

Also f(0) = 1, f’(0) = 1, f’’(0) = 1

Since (d/dx)e^x = e^x

Therefore, f’(x) = e^x

F’’(x) = e^x

F’’’(x) = e^x

Now, f(0+h) = f(0) + f’(0)h + f’’(0)h²/2! + f’’’(0)h³/3!

F(h) = 1 + h + h²/2 + h³/6 + h⁴/24 + …

x+h = 0 +h, ( or replace h by x).

f(x) = 1 + x + x²/2 + x³/6 + x⁴/24 + ….

Or, This can be simplified as maclaurin series.

e^x =1 + x + x²/2! + x³/3! + ……

Suggested:

Linear regression

What is Maclaurin Series