### 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

# Arithmetic Progression (A.P.)

If (constant), for , then is called an Arithmetic Sequence or an Arithmetic Progression and the series is called an Arithmetic Series. The constant is known as the common difference which may be positive or negative.

Partial Sum of an Arithmetic Series -:

If is an Arithmetic series, then which is same as , where ,

Common difference , then of the finite series .

Therefore or according as or .

If or according as or .

This shows that an Arithmetic Series always diverges, except the special case when .

In this case for all so that sum of the corresponding Arithmetic Series is zero.

Note -:

Sum of the First all Counting Number -:

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