Sigma Notation

The Greek letter S (read as sigma) denotes the sum. When written before the n^th term of series, implies, the sum of all terms obtained by giving to n the different values 1,2,3…n. Thus,

Examples:

1. Find the sum to the series 1+2x+3x²+.... to n terms and to infinity when x < 1.

Suggested answer:

Subtracting (ii) from (i), we get

2. Find the sum to n terms of the series

Suggested answer:

n^th term of (1,2,3,....) is n

Subtracting (ii) from (i), we get

3. Find the sum to infinity of the series

Suggested answer:

Subtracting (ii) from (i), we get

4. Sum the following:

i) 1.2 + 2.4 + 3.8 +.... to n terms

Suggested answer:

i) 1.2 + 2.4 + 3.8 +.... to n terms

The n^th term of (1,2,3,....n) is n.

The n^th term of (2,4,8,...) is

The n^th term of the given series is n2ⁿ

Subtracting (ii) from (i), we have

Subtracting (ii) from (i), we have

Though it is not an arithmetic-geometric series, we can apply a similar method.

Subtracting (ii) from (i),

Subtracting (iv) from (iii),

Subtracting (ii) from (i),

find d.

Suggested answer:

Subtracting (ii) from (i), we get

Suggested answer: