What is the sum of the first $20$ terms of the sequence $0.7, 0.77, 0.777, \dots$?

If the $n^{th}$ term of a series is $n(n + 1)$,then the sum of its $n$ terms is......

Let $a_1, a_2, a_3, \ldots$ be an arithmetic progression with $a_1=7$ and common difference $8$. Let $T_1, T_2, T_3, \ldots$ be such that $T_1=3$ and $T_{n+1}-T_n=a_n$ for $n \geq 1$. Then,which of the following is/are $TRUE$?
$(A) T_{20}=1604$
$(B) \sum_{k=1}^{20} T_k=10510$
$(C) T_{30}=3454$
$(D) \sum_{k=1}^{30} T_k=35610$

The sum of the series $1^2 + 2(2^2) + 3^2 + 2(4^2) + 5^2 + 2(6^2) + \dots + 2(2m)^2$ is

The sum $1 + \frac{1}{2}(1^2+2^2) + \frac{1}{3}(1^2+2^2+3^2) + \dots$ up to $10$ terms is equal to:

If $1^4+2^4+3^4+\ldots+n^4=f(n) \left(1^2+2^2+\ldots+n^2\right)$,for all $n \in N$,then $f(4)$ is equal to