Math Assignment Help With Arithmetic Series

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)

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