Serie De Potencias Importantes

Stat 401: Introduction to Probability

Handout-05, September 27, 2006

Source:http://www.maths.manchester.ac.uk/~cds/internal/tables/tables.html

Special Power Series

x 2 x3
xr
e =1+x+
+
+ ... +
+ ...
2!
3!
r!
x

(all x)

sin x = x −

x 3x5 x 7
(−1)r x2r+1
+
−
+ ... +
+ ...
3!
5!
7!
(2r + 1)!

(all x)

cos x = 1 −

x 2 x4 x 6
(−1)r x2r
+
−
+ ... +
+...
2!
4!
6!
(2r)!

(all x)

tan x = x +

x3 2x5 17x7
+
+
+ ...
3
15
315

(|x| < π )
2

1 x3 1.3 x5 1.3.5 x7
++
+
23
2.4 5
2.4.6 7

sin−1 x = x +

... +
tan−1 x = x −

1.3.5....(2n − 1) x2n+1
+ ...
2.4.6....(2n) 2n + 1

x3 x 5x7
x2n+1
+
−
+ ... + (−1)n
+ ...
3
5
7
2n + 1

n(1 + x) = x −

(|x| < 1)
(|x| < 1)

xn
x 2 x 3 x4
+
−
+ ... +(−1)n+1 + ... (−1 < x ≤ 1)
2
3
4
n

sinh x = x +

x 3 x 5 x7
x2n+1
+
+
+ ... +
+ ...
3!
5!
7!
(2n + 1)!

(all x)cosh x = 1 +

x2 x4 x6
x2n
+
+
+ ... +
+ ...
2!
4!
6!
(2n)!

(all x)

tanh x = x −

x3 2x5 17x7
+
−
+ ...
3
15315

(|x| < π )
2

sinh−1 x = x −

1 x3 1.3 x5 1.3.5 x7
+
−
+
23
2.4 5
2.4.6 7

... + (−1)n
tanh−1 x = x +1.3.5...(2n − 1) x2n+1
+ ...
2.4.6...2n 2n + 1

x2n+1
x3 x 5 x 7
+
+
+ ...
+ ...
3
5
7
2n + 1

(|x| < 1)
(|x| < 1)