Page 132 - 6099

Appendix D

Table of Sums

∞
X r
n
r = , for |r| < 1
1 − r
n=1
N N+1
X r − r
n
r =
1 − r
n=1
b
X (a + b)(b + 1 − a)
n =
2
n=a
N
X N(N + 1)
n =
2
n=1
b
X 2 b(b + 1)(2b + 1) − a(a − 1)(2a − 1)
n =
6
n=a

N
X 2 N(N + 1)(2N + 1)
n =
6
n=1
∞ n+1
X (−1)
= log(2)
n
n=1
∞ 2
X 1 π
=
n 2 6
n=1
∞ n+1 2
X (−1) π
=
n 2 12
n=1

125