Match List I with List II

List I

List II

A.

Series \(\rm \sum_{n=1}^∞ \frac{1}{n^{\frac{3}{2}}}\) is

I.

Monotone and convergent both

B.

Series \(\rm \sum_{n=1}^∞ \frac{3^n}{n^{^2}}\) is

II.

e^-2

C.
\(\rm \lim_{n\rightarrow ∞}\left(\frac{n+1}{n+2}\right)^{2n+1}\)
III.

Divergent to ∞

D.

Sequence \(\rm x_n=1+\frac{1}{2!}+\frac{1}{3!}+....+\frac{1}{n!}\) for n ∈ N

IV.

Convergent

Choose the most appropriate answer from the options given below:

A - IV, B - III, C - II, D - I

A - III, B - IV, C - I, D - II

A - I, B - II, C - III, D - IV

A - IV, B - I, C - III, D - II

List I		List II
A.	Series \(\rm \sum_{n=1}^∞ \frac{1}{n^{\frac{3}{2}}}\) is	I.	Monotone and convergent both
B.	Series \(\rm \sum_{n=1}^∞ \frac{3^n}{n^{^2}}\) is	II.	e^-2
C.	\(\rm \lim_{n\rightarrow ∞}\left(\frac{n+1}{n+2}\right)^{2n+1}\)	III.	Divergent to ∞
D.	Sequence \(\rm x_n=1+\frac{1}{2!}+\frac{1}{3!}+....+\frac{1}{n!}\) for n ∈ N	IV.	Convergent