calculus question help

Question

Find the limit of the sequence of partial sums whose general term is  .

	10
	0
	1
	Does not exist

Answer 1

The answer is e¹⁰.

Think of the Taylor series for e^x about 0. The derivative of all orders is e^x , which is 1 evaluated at x = 0. Sum this and you can verify. So you don't have overflow issues, start with 1 at n= 0 and multiply the preceding term by 10/n. Add 40 terms and you will be convinced.