5.8 Arithmetic Series

1. i) For {0, 1, 2, 3, 4}, with the formula a_n = n - 1

The finite series is 0 + 1 + 2 + 3 + 4.

Σ(i – 1) = 0 + 1 +2 + 3 + 4 = 10

i = 1

In summation notation it can be written as above.

Formula;

a_n = a_n -1 + 1

1. ii) The finite series is 0 + 1 + 2 + 3 + 4 + . . .

In summation notation we write

∞

Σ(n – 1) = 0 + 1 +2 + 3 + 4 +…..

n = 1

For the alternating infinite sequence -1, 2, -3, 4, -5, . . ., the formula is

a_n = (-1)_nn

1. iii) The finite series is -1 + 2 - 3 + 4 -. . .

In summation notation we write it as;

∞

Σ(– 1)ⁿ n = - 1 +2 - 3 + 4 - …..

i = 1

For the alternating infinite sequence -1, 2, -4, 8, -16, 32, . . .,

the formula is

an = (-1)ⁿ (2)ⁿ - 1

General Formula:

S_n = (a1 + a_n) (n) = n (a1 + a_n)

22

Email Based Assignment Help in Arithmetic Series

To submit Arithmetic Series assignment click here.

Following are some of the topics in Sequences Of Numbers And Series in which we provide help: