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Appendix D

Table of Sums

∞
X r
n
r = , for |r| < 1
1 − r
n=1

N N+1
X n r − r
r =
1 − r
n=1

b
(a + b)(b + 1 − a)
X
n =
2
n=a

N
N(N + 1)
X
n =
2
n=1

b
X b(b + 1)(2b + 1) − a(a − 1)(2a − 1)
2
n =
6
n=a

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

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

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