List of top Mathematics Questions on Principle of Mathematical Induction asked in CUET (PG)

If \(f(z)=\frac{1}{z^2-3z+2}\)is expanded in the region |z|<1, then
The given series \(\frac{x}{1.3}+\frac{x^2}{2.4}+\frac{x^3}{3.5}+......,(x\gt0)\)is convergent in the interval
The infinite series \(\displaystyle\sum_{n=1}^{∞} (1+\frac{1}{n})^{-n^2}\) is:
The infinite series \(\displaystyle\sum_{n=1}^{∞} \frac{3^n}{4^{n+2}}\) is:
Match List I with List II
LIST I LIST II
A.Series \(\displaystyle\sum_{n=1}^{∞} \frac{1}{n^\frac{3}{2}}\) isI.Monotone and 
convergent both
B.Series \(\displaystyle\sum_{n=1}^{∞} \frac{3^n}{n^2}\) isII.\(e^{-2}\)
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∈NIV.Convergent
Choose the correct answer from the options given below:
The value of \(\lim\limits_{n \to \infty} \frac{1}{n} [1+2^{\frac{1}{2}}+3^{\frac{1}{3}}+...n^{\frac{1}{n}}]\) is