# What is the sum of the series #1+ln2+(((ln2)^2)/(2!))+...+(((ln2)^n)/(n!))+...#?

2

By definition of the exponential function:

Look at the pattern:

And so you are evaluating:

By signing up, you agree to our Terms of Service and Privacy Policy

The sum of the series is e^ln(2) = 2.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you apply the ratio test to determine if #Sigma 1/sqrtn# from #n=[1,oo)# is convergent to divergent?
- Does the Alternating Series Test determine absolute convergence?
- How do you find #\lim _ { x \rightarrow \infty } \sqrt { x ^ { 2} + 1x - 4} - x#?
- How do you find #a_1# for the geometric series with #r=3# and #s_6=364#?
- How do you find #lim cos(3theta)/(pi/2-theta)# as #theta->pi/2# using l'Hospital's Rule?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7