Further Pure Mathematics

1. Further Pure Mathematics Notes
1.1 Logarithmic Functions and Indices>1.2 The Quadratic Function>1.3 Identities and Inequalities>1.4 Graphs>1.5 Series>1.6 The Binomial Series>1.7 Scalar and Vector Quantities>1.8 Rectangular Cartesian Coordinates>1.9 Calculus>1.10 Trigonometry>

Find sum when lower limit is NOT 1:

S upper limit – S lower limit – 1

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers that increase or decrease by the same amount. This amount is called common difference.

Arithmetic Series

An arithmetic series is the sum of the terms in an arithmetic sequence.

Geometric Sequence

A geometric sequence is a sequence of numbers that increase or decrease by a common ratio.

Geometric Series

An geometric series is the sum of the terms in an geometric sequence.

Type 1: Geometric Series (Finite)

Type 2: Geometric Series (Infinite)

If |r| < 1, then rⁿ approaches 0 for very large n.

We say that the series converges. We call this the limiting sum of the series.