INFINITE SERIES

Some important questions with solutions of infinite series

Topics to be covered

Sequences, Series, General properties, series of positive terms, comparison test, Integral test, Comparison of ratios, Dalemberts ratio test, Raabe`s test, Logarithmic test, Cauchy`s root test, Alternating series, Leibnitz`s rule Power series

Overview of chapter or Short notes of infinite series

1.

A sequence is a succession of numbers or terms formed according to some definite rule. The 
nth term in a sequence is denoted by un. 
For example, if un = 2n + 2
By giving different values of n in un, we get different terms of the sequence. 
Thus, u1 = 4, u2 = 6.
A sequence having unlimited number of terms is known as an infinite sequence

2.

CONVERGENT SEQUENCE If the limit of a sequence is finite, the sequence is convergent. If the limit of a sequence does not tend to a finite number, the sequence is said to be divergent. e.g. 1 + 1/2 + 1/3 + 1/4 . is a convergent sequence. 3, 5, 7, ..., (2n + 1), ... is a divergent sequence.