B.Sc Method Chapter 8 (Infinite Series) Notes

Mathematical Methods (B.Sc.)

Chapter:08 (Infinite Series)

In this chapter, we will study the following topics:

• finite sequence
• infinite sequence
• terms of sequence
• divergent sequence
• properties of sequence
• bounded sequence
• a divergent test
• monotonic sequence
• non-decreasing sequence
• non-increasing sequence
• strictly increasing sequence
• strictly decreasing sequence
• monone sequence
• a bounded monotonic sequence is convergent
• nth term of series
• geometric series
• cauchy criterion
• harmonic series
• positive term series
• the basic comparison test
• the divergence test
• the limit comparison test
• the integral test
• cauchy integral’s test theorem
• the ratio test
• cauchy root test
• alternating series
• absolute and conditional convergence
• the root test for absolute convergence
• power series
• convergence of power series
• interval of convergence
• radius of convergence
• differential and integration of power series
• power series representations
• Gregory’s series
• addition an multiplication of power series

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