Question

Let f be the function given by f(x) = e^x/2
Find the first three nonzero term and the general term around 0 for (e^x/2)-1)/x
Use it to find g'(2) and use it to show that

Answer 1

\[\sum_{n=0}^{\infty} n/ 4(n+1)! = 1/4\]

Answer 2

I actually found the first three nonzero terms but don't understand the second part.

Answer 3

Help please!

Answer 4

Is it
\[ \frac{ e^x} 2
\]

Answer 5

What is g(x)?

Answer 6

g(x) is the ((e^x/2 )-1)/x

Answer 7

take the derivative of \(\frac{e^{\frac{x}{2}}-1}{x}\) i think is the first step,then replace x by 2

Answer 8

derivative evaluated at 2 will give you \(\frac{1}{4}\) which means that the expansion evaluated at two (that infinite sum you have in the question) must also be \(\frac{1}{4}\)

Answer 9

How do we do that?

Answer 10

FOr the last part.

Answer 11

how do you do what?

Answer 12

Make the expansion evaluated at 2 = 1/4. If I plug it in, I get like some crazy fraction. How do you make the sum = 1/4