Задача 6.

Using induction, show the following: a) $1+\ldots+n=\frac{n(n+1)}2$; b) $1+\ldots+n^2=\frac{n(n+1)(2n+1)}6$; c) $1+\ldots+n^3=\frac{n^2(n+1)^2}4$.