How to express the following as a series? How you you express $$1+3+6+10+15+21+28+...$$ as a summation? I've tried different ways but they were wrong and always brought me back to square one. Thanks!

$$S_n=1+3+6+10+15+\cdots+T_n$$
$$S_n=1+3+6+10+15+\cdots+T_{n-1}+T_n$$
On subtraction, $$0=1+(3-1)+(6-3)+(10-6)+(15-10)+\cdots+(T_n-T_{n-1})-T_n$$
$$\implies T_n=1+2+3+\cdots\text{up to }n\text{ terms}=\frac{n(n+1)}2$$
$$\text{Now, }(r+1)^3-r^3= 6\frac{r(r+1)}2+1$$ (Observe the Telescoping Sum in the Left Hand Side)
Putting $r=1,2,\cdots,n-1,n$ and adding them we get, 
 $$(n+1)^3-1=6S_n+n$$
$$\implies 6S_n=n^3+3n^2+3n+1-1-n=n^3+3n^2+2n=n(n+1)(n+2)$$
