Find the Maclaurin series for e^10x^2

Question

Write in series notation.

This is what I got so far
f(x)=f(0)+(f'(0)/1!)(x)+(f"(0)/2!)(x)^2+(f"'(0)/3!)(x)^3

e^10x^2=1+1x+(1/2!)x^2+(1/3!)x^3
I am stuck, I don't think I am going this right. How would you write the notation

Answer 1

In google paste:

Maclaurin series calculator eMathHelp

When you see list of results click on:

Taylor and Maclaurin (Power) Series Calculator - eMathHelp

When page be open in rectangle Enter a function type your function.

If your function is:

e^(10x^2)

type it like that

In rectangle Order n =

type whatever number you want.

The default value is 5 but you can choose 6, 7, 8 etc.

Then click option: CALCULATE

You will see the solution step by step

Answer 2

You want
∑ (10x^2)^k/k! = 1 + 10x^2 + 50x^4 + ...