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# Chapter 08: Infinite Series

Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN.

Infinite series are of great importance in both pure and applied mathematics. They play a significant role in Physics and engineering. In fact many functions can be represented by infinite series. The theory of infinite series is developed through the use of special kind of function called sequence.

### Contents and summary

- Sequences
- Infinite series
- The basic comparison test
- The limit comparison test
- The integral test
- The ratio test
- Cauchy's root test
- Alternating series
- Absolute and conditional convergence
- Power series
- Convergence of power series
- Differentiation and integration of power series
- Addition and multiplication of power series

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