- Finite Sums and Infinite Series

Arithmetic-geometric progression:

(a+ bk)qk = a(1− qn)− b(n− 1)qn

1− q + bq(1− qn−1) (1− q)2 .

k = n(n+ 1)

2 .

2. n∑

k2 = 1

6 n(n+ 1)(2n + 1).

3. n∑

k3 = 1

4 n2(n+ 1)2.

4. n∑

k4 = 1

30 n(n+ 1)(2n + 1)(3n2 + 3n− 1).