1a) Find a simple expression for the following sum: $$\sum_{k=1}^n (a_k - a_{k-1}) $$
1b) Find $$\sum_{k=1}^n (k^3 - (k-1)^3). $$
1c) Show that $$\sum_{k=1}^n k^2 = \frac{n(n + 1)(2n+1)}{6}$$ WITHOUT using induction method but by using the definition formula: $$\sum_{k=1}^n k= \frac{n(n + 1)}{2}$$
Any guidance would be great with any of these questions if you have time. No similar examples of these questions were in the textbook so I needed clarification on how to solve these type of questions. Thank you very much.
Hint for (a) and (b): try writing out the sum without sigma notation. $$\sum_{k=1}^n(a_k-a_{k-1})=\sum_{k=1}^n(-a_{k-1}+a_k)=-a_0+\color{blue}{a_1-a_1}+\color{red}{a_2-a_2}+\dots+\color{green}{a_{n-1}-a_{n-1}}+a_n={}?$$