The sum of the series: $(2)^2 + 2(4)^2 + 3(6)^2 + \dots$ up to $10$ terms is

The sum of the series $\frac{2^{3}-1^{3}}{1 \times 7}+\frac{4^{3}-3^{3}+2^{3}-1^{3}}{2 \times 11}+\frac{6^{3}-5^{3}+4^{3}-3^{3}+2^{3}-1^{3}}{3 \times 15}+\ldots + \frac{30^{3}-29^{3}+\ldots+2^{3}-1^{3}}{15 \times 63}$ is equal to:

The sum of the series $3 + 33 + 333 + \dots$ to $n$ terms is

The sum of $n$ terms of the following series $1 \times 2 + 2 \times 3 + 3 \times 4 + 4 \times 5 + \dots$ is:

Find the sum of the series $1 + 3 + 7 + 15 + 31 + \dots$ up to $n$ terms.

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