Here you need to start with
a(n)
=
1 + 2 + 3 + ... + n
=
1
2
 n(n+1)
b(n)
=
12 + 22 + 32 + ... + n2
=
1
6
 n(n+1)(2n + 1)
c(n)
=
13 + 23 + 33 + ... + n3
=
1
4
 n2(n+1)2.

These are well known results found in many text books and you will find proofs in some problems on this website. See Picture Story and Natural Sum.