# 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.