How to evaluate : $\lim_{n \to \infty}\sum_{k=0}^{n} \frac{{n\choose k}}{n^k(k+3)}$
5521
Evalute $ \lim_{n\rightarrow \infty}\sum^{n}_{k=0}\frac{\binom{n}{k}}{n^k(k+3)} $
39034
How would you evaluate $\liminf\limits_{n\to\infty} \ n \,|\mathopen{}\sin n|$
41911
Use Riemann integral to evaluate the limit $\lim_{n \rightarrow \infty} \frac{\sum_{k=1}^n \sqrt{k}}{\sum_{k=1}^n \sqrt{n+k}}$
154506
Evaluating $\lim_{n\rightarrow\infty} (\frac{(1+\frac{1}{n})^n}{e})^n$
17872
Evaluate $\lim\limits_{n\to\infty}\frac{\sum_{k=1}^n k^m}{n^{m+1}}$
4638
What is the value of $\lim_{n\to \infty} \sum_{j=n}^{4n} {4n \choose j}\bigl(\frac{1}{4}\bigr)^{j} \bigl(\frac{3}{4}\bigr)^{4n-j}$?
30063
How do you calculate this limit $\lim_{n\to\infty}\sum_{k=1}^{n} \frac{k}{n^2+k^2}$?
152557
Calculate $ \lim\limits_{n \to \infty} \sum\limits_{k=0}^n \frac{2^{k-1}}{a^{2k-1}+1} $
131456
Calculate $\lim_{n\to\infty} \sum_{k=1}^{n} \Big(\frac{k}{n}\Big)^{\alpha k}$
157539
Prove: $\lim\limits_{n\to\infty}\frac{1}{n}\sum\limits_{k=1}^{n}\sqrt{1+\frac{k}{n}}=\frac{2}{3}(2\sqrt{2}-1)$
72842
Evaluation of the limit $\lim\limits_{n \to \infty } \frac1{\sqrt n}\left(1 + \frac1{\sqrt 2 }+\frac1{\sqrt 3 }+\cdots+\frac1{\sqrt n } \right)$
136444
Evaluating $\sum_{n=0}^\infty\frac{(-1)^n}{3n+1}$
81090
Calculate $\lim_{n\to\infty}(\sqrt{n^2+n}-n)$.
137155
Sum $ \sum\limits_{k=1}^{\infty} \frac{k^2}{2^k}$
105860
Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$
83634
Find $\lim_{n\to \infty}\sqrt[n]{3^n+5^n}$
90773
$\lim_{n\rightarrow\infty}\frac{1}{n}\sum_{k=1}^{n}\frac{k}{k^{2}+1}$