Question

Solve the problem in the attachment with proper explanation

Thank You ​

Answer 1

Given,

1 + i² + i⁴ + .... + i²ⁿ.

Solution,

Clearly the given Series is in G.P with,

First term a = 1

Common ratio r = i²/1 = i² = -1.

Calculate Sum of n terms of GP.

• Sₙ = a[1 - rⁿ/1 - r]

==> 1[1 - (-1)ⁿ⁺¹/1 - (-1)]

==> [1 - (-1)ⁿ⁺¹/1 + 1]

==> [1 - (-1)ⁿ * (-1)¹/2]

==> [(-1)ⁿ + 1]/2

Result,

Sₙ = [(-1)ⁿ + 1]/2

Answer 2

Answer:

Step-by-step explanation: