Question

Evaluate the series 1+x/2+x²/2+x³/3+......x¹⁰⁰/100.?

A) eˣ
B) eˣ²
C) In(x)
D) 1/eˣ

Answer 1

The series 1+x/2+x²/2+x³/3+...+x¹⁰⁰/100 is equal to e^x.

Step-by-step explanation:

To evaluate the series 1+x/2+x²/2+x³/3+...+x¹⁰⁰/100, we can rewrite it as:

1 + (x/2) + (x²/2) + (x³/3) + ... + (x¹⁰⁰/100)

We can recognize that each term in the series is actually a term from the expansion of the function e^x. So, the series is equal to:

e^x

Therefore, the correct answer is option A) eˣ.