Page 488 - Applied Numerical Methods Using MATLAB

APPENDIX F

USEFUL FORMULAS

Formulas for Summation of Finite Number of Terms
N N+1 N N N+1
1 − a 1 − (N + 1)a + Na
n n
a = (F.1) na = a (F.2)
1 − a (1 − a) 2
n=0 n=0
N N
N(N + 1) N(N + 1)(2N + 1)
2
n = (F.3) n = (F.4)
2 6
n=0 n=0
N
N(N + 1)(N + 2)

n(n + 1) = (F.5)
3
n=0
N
NP n N!
N N−n n
(a + b) = NC n a b with NC n = NC N−n = = (F.6)
n! (N − n)!n!
n=0
Formulas for Summation of Infinite Number of Terms
∞ ∞
1 x
n n
x = , |x| < 1 (F.7) nx = , |x| < 1 (F.8)
1 − x (1 − x) 2
n=0 n=0
∞ k
∂ x
k n
n x = lim(−1) k , |x| < 1 (F.9)
a→0 ∂a k x − e −a
n=0
∞ n
(−1) 1 1 1 1

= 1 − + − + ··· = π (F.10)
2n + 1 3 5 7 4
n=0
(continued overleaf )

Applied Numerical Methods Using MATLAB , by Yang, Cao, Chung, and Morris
Copyright  2005 John Wiley & Sons, I nc., ISBN 0-471-69833-4

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