Question

Arithmetic geometric progression solved examples

Answer 1

Find the sum of series 1. 2 + 2. 22 + 3. 23 +…+ 100. 2100.

Solution: Let us denote the given series by S.

Let S = 1.2 + 2.22 + 3.23 +…+ 100.2100                           …… (1)

⇒ 2S = 1.22 + 2.23 +…+ 99.2100 + 100.2101                      …… (2)

⇒ –S = 1.2 + 1.22 + 1.23 +…+ 1.2100 – 100.2101

⇒ –S = 1.2 (299–1/(2–1)) – 100.2101

⇒ S = –2100 + 2 + 100.2101 = 199.2100 + 2.