I have som question about sums never done them before, didnīt know where to post it its a analysis course so they cant be to misplaced (i hope). Am I on the right track or doing someting completely wrong? All tips appreciated..$\displaystyle \Rightarrow$(Clapping)

Write the following using Sigma notation:

$\displaystyle 1*2*3+2*3*4+3*4*5+...+101*102*103$

$\displaystyle \sum_{k=1}^{101}(k)(k+1)(k+2)$

2)

$\displaystyle 1*2+2*2^2+3*2^3+...+10*2^{10}$

$\displaystyle \sum_{k=1}^{10}k\times2^k$

3)

then we have $\displaystyle 1+4+9+16...+100$

$\displaystyle \sum_{k=1}^{10}(n^k)$

and finaly

4)

$\displaystyle \frac{1}{1\times 3}+\frac{1}{2\times 4}+\frac{1}{3\times 5}...$

$\displaystyle \sum_{k=1}^{\infty} \frac{1}{k\times (k+2)}$

Actually what does this mean

$\displaystyle \sum_{k=1}^{n} \frac{k}{n+k}$ n is suppose to be the final value. The exercis said write without Sigma notation. My question is does n=k so its $\displaystyle \frac{1}{1+1}+\frac{2}{2+2}+\frac{3}{3+3}$ ?