In the earlier classes we studied about the sum of a few terms, like sum of first n terms, of arithmetic and geometric progressions.

**Finite Series**

**1. Sum of
Arithmetic, Geometric and Arithmetico-Geometric Progressions**

In the earlier classes we studied
about the sum of a few terms, like sum of first *n* terms, of arithmetic and
geometric progressions. We now recall them.

** **

**Sum of
Arithmetic and Geometric Progressions**

**Sum of
Arithmetico-Geometric Progressions**

**2. Telescopic
Summation for Finite Series**

Telescopic summation is a more
general method used for summing a series either for finite or infinite terms.
This technique expresses sum of *n* terms of a given series just in
two terms, usually first and last term, by making the intermediate terms cancel
each other. After canceling intermediate terms, we bring the last term which is
far away from the first term very close to the first term. So this process is
called “Telescopic Summation”.

**3. Some Special Finite Series**

In this section we give some of
the important formulas of summing up finitely many terms which follows either
an AP, GP, or any specific series.

Note that the above three results
were proved in the earlier classes.

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11th Mathematics : UNIT 5 : Binomial Theorem, Sequences and Series : Finite Series | Definition, Formula, Solved Example Problems, Exercise | Mathematics