If $2^3+4^3+6^3+\ldots+(2n)^3=h n^2(n+1)^2$,then $h$ is equal to

The number of positive integers $n$ in the set $\{1, 2, 3, \ldots, 100\}$ for which the number $\frac{1^2+2^2+3^2+\ldots+n^2}{1+2+3+\ldots+n}$ is an integer is

Let $\alpha = \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \dots \infty$ and $\beta = \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \dots \infty$. Then the value of $(0.2)^{\log_{\sqrt{5}}(\alpha)} + (0.04)^{\log_{5}(\beta)}$ is equal to:

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

For any integer $n \geq 1$,the sum $\sum_{k=1}^n k(k+2)$ is equal to

Write the first five terms of the sequence whose $n^{th}$ term is $a_{n} = n(n+2)$.