Method of Difference - Practice Questions & MCQ

The sum of the series

is equal to:

 In a triangle , if is and medians through and are and  respectively, then is:

If $t_n$ denotes the $n^{\text {th }}$ term of the series $2+3+6+11+18+\ldots$ then $t_{50}$ is

The sum of

$(1^{2}-1+1)(1!)+(2^{2}-2+1)(2!)+...+(n^{2}-n+1)(n!)$

is

Let $\mathrm{S}_{\mathrm{n}}=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\ldots$ upto n terms. If the sum of the first six terms of an A.P. with first term p and common difference p is $\sqrt{2026 \mathrm{~S}_{2025}}$, then the absolute difference between $20^{\text {th }}$ and $15^{\text {th }}$ terms of the A.P. is

The value of $\lim _{n \rightarrow \infty}\left(\sum_{K=1}^n \frac{k^3+6 k^2+11 k+5}{(k+3)!}\right)$ is: