MHB Fast Calculation [sum] problem

[susanto3311]

hello all...

would you help me out, how to sum 3 questions problem..

please, see my picture attachment..

thanks for your helping...

susanto3311

 

[MarkFL]

There are 3 formulas you can use here:

[box=blue]

Summation Formulas​

$$\sum_{k=1}^n\left(k\right)=\frac{n(n+1)}{2}\tag{1}$$

$$\sum_{k=1}^n\left(k^2\right)=\frac{n(n+1)(2n+1)}{6}\tag{2}$$

$$\sum_{k=1}^n\left(k^3\right)=\left(\frac{n(n+1)}{2}\right)^2\tag{3}$$[/box]

Can you identify $n$ in each case and find the sums?