If $\sum\limits_{i = 1}^n i = \frac{n(n + 1)}{2}$,then $\sum\limits_{i = 1}^n (3i - 2) = $

If $f(1)=3$, and $f(n+1)-f(n)=3(4^n-1)$, then for all $n \in N$, $f(n)=$

Let $\{a_{n}\}_{n=1}^{\infty}$ be a sequence such that $a_{1}=1, a_{2}=1$ and $a_{n+2}=2a_{n+1}+a_{n}$ for all $n \geq 1$. Then the value of $47 \sum_{n=1}^{\infty} \frac{a_{n}}{2^{3n}}$ is equal to $.....$

The sum of the first $9$ terms of the series $\frac{1^3}{1} + \frac{1^3 + 2^3}{1 + 3} + \frac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \dots$ is:

Find the $20^{\text{th}}$ term of the series $2 \times 4 + 4 \times 6 + 6 \times 8 + \dots$ up to $n$ terms.

What is the sum of the first $10$ terms of the series $0.7 + 0.77 + 0.777 + \dots$?