A Table of Power Series
1−xN+1 2 N 1�∞n 1−x =1+x+x +…+x 1−x= x
n=0 ∞∞
1 = �anxn 1 = �xrn 1−ax 1−xr
n=0� � � � n=0
(1+x)r = ∞ r xn where m =m(m−1)···(m−k+1) n=0n k k!
1 =�∞ �n+r−1�xn
(1−x)r n n=0
√
1+x=
�∞ �2n� (−1)n+1 n
e x = �∞ x n n=0 n!
�∞ x2n+1
= (2n + 1)! n=0
n=0
n 4n(2n−1)x
ex +e−x �∞ x2n cosh(x) = 2 = (2n)!
n=0
sinh(x) =
ex −e−x 2

A Table of Power Series
1−xN+1 2 N 1�∞n 1−x =1+x+x +…+x 1−x= x
n=0 ∞∞
1 = �anxn 1 = �xrn 1−ax 1−xr
n=0� � � � n=0
(1+x)r = ∞ r xn where m =m(m−1)···(m−k+1) n=0n k k!
1 =�∞ �n+r−1�xn
(1−x)r n n=0
√
1+x=
�∞ �2n� (−1)n+1 n
e x = �∞ x n n=0 n!
�∞ x2n+1
= (2n + 1)! n=0
n=0
n 4n(2n−1)x
ex +e−x �∞ x2n cosh(x) = 2 = (2n)!
n=0
sinh(x) =
ex −e−x 2