Match List I with List II LIST I LIST II A . Series $\displaystyle\sum_{n=1}^{∞} \frac{1}{n^\frac{3}{2}}$ is I . Monotone and convergent both B . Series $\displaystyle\sum_{n=1}^{∞} \frac{3^n}{n^2}$ is II . $e^{-2}$ C . $\lim\limits_{n \to \infty} (\frac{n+1}{n+2})^{2n+1}$ III . Divergent to ∞ D . sequence $x_n=1+\frac{1}{2!}+\frac{1}{3!}+…\frac{1}{n!}$ for n∈N IV . Convergent Choose the correct answer from the options given below:

Question

Match List I with List II LIST I   LIST II A . Series  $\displaystyle\sum_{n=1}^{∞} \frac{1}{n^\frac{3}{2}}$  is I . Monotone and  convergent both B . Series  $\displaystyle\sum_{n=1}^{∞} \frac{3^n}{n^2}$  is II . $e^{-2}$ C . $\lim\limits_{n \to \infty} (\frac{n+1}{n+2})^{2n+1}$ III . Divergent to ∞ D . sequence  $x_n=1+\frac{1}{2!}+\frac{1}{3!}+…\frac{1}{n!}$  for n∈N IV . Convergent Choose the correct answer from the options given below:

cdquestions Admin · Accepted Answer

The correct option is(A):A IV, B III, C II, D I

Answer

A IV, B III, C II, D I

Answer

A III, B IV, C I, D II

Answer

A I, B II, C III, D IV

Answer

A IV, B I, C III, D II

	LIST I		LIST II
A.	Series \(\displaystyle\sum_{n=1}^{∞} \frac{1}{n^\frac{3}{2}}\) is	I.	Monotone and convergent both
B.	Series \(\displaystyle\sum_{n=1}^{∞} \frac{3^n}{n^2}\) is	II.	\(e^{-2}\)
C.	\(\lim\limits_{n \to \infty} (\frac{n+1}{n+2})^{2n+1}\)	III.	Divergent to ∞
D.	sequence \(x_n=1+\frac{1}{2!}+\frac{1}{3!}+…\frac{1}{n!}\) for n∈N	IV.	Convergent

The Correct Option is A

Solution and Explanation

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