For any integer $n \geq 1$,$\sum_{K=1}^n K(K+2) =$

The sum of the first $20$ terms of the series $5+11+19+29+41+\ldots$ is $..........$.

The sum of the $1^{st} n$ terms of the series $\frac{1^{2}}{1} + \frac{1^{2}+2^{2}}{1+2} + \frac{1^{2}+2^{2}+3^{2}}{1+2+3} + \ldots$ is:

If $\sum_{r=1}^{n}r^3 - \sum_{p=1}^{n}\sum_{m=1}^{p}\sum_{r=1}^{m}1 = 80$,then the possible value of $n$ is:

If $0 < \theta, \phi < \frac{\pi}{2}$,$x = \sum_{n=0}^{\infty} \cos^{2n} \theta$,$y = \sum_{n=0}^{\infty} \sin^{2n} \phi$,and $z = \sum_{n=0}^{\infty} \cos^{2n} \theta \cdot \sin^{2n} \phi$,then:

Let $S_n = \sum_{k=1}^{4n} (-1)^{\frac{k(k+1)}{2}} k^2$. Then $S_n$ can take the value$(s)$:
$(A) 1056$
$(B) 1088$
$(C) 1120$
$(D) 1332$