Engineering Mathematics

Sunday, April 17, 2011

examples of Geometric Series

Perquisites :

1. Geometric Series

Example (1)

$1-2x+4x^{2}-8x^{3}+\cdot \cdot \cdot+(-2x)^{n} =\sum _{n=0}^{\infty }(-2x)^{n}=\frac{1}{1+2x}$

if x=1

$1-2+4-8+\cdot \cdot \cdot+(-2)^{n}=\frac{1}{3}$

if x=-1

$1+2+4+8+\cdot \cdot \cdot+(2)^{n}= -1$

Posted by AHM at 12:51 AM

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Labels: geometric series, number theory

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