### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Geometric Progression (G.P.)

If  (constant), for then is called a Geometric Sequence or Geometric Progression (G.P). and the series is called a geometric series. The constant is known as the common ratio .

Note -:

(i) If , common ratio , then

(ii) No term of a GP can be zero, for otherwise will be meaningless for the corresponding value of .

Partial Sum of a Geometric Series -:

For a geometric series with and common ratio ratio ,

, for

If , then , for every , so that

Sum of Geometric Series -:

If < , i.e. < < then . When . So for the geometric series with < .

We have

Therefore ; if < and diverges if .

Hence the geometric series converges if <  and diverges if .

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