Supplement 2. Finite Sums and Infinite Series

Arithmetic progression:

1. n-1∑ k=0

(a + bk) = an + bn(n – 1) 2

.

Geometric progression:

2. n∑

aqk-1 = a qn – 1 q – 1

.

Arithmetic-geometric progression:

3. n-1∑ k=0

(a + bk)qk = a(1 – q n) – b(n – 1)qn 1 – q

+ bq(1 – qn-1)

(1 – q)2 .