A gardener wanted to reward a boy for his good deeds by giving some mangoes. He gave the boy two choices. He could either have 1000 mangoes at once or he could get 1 mango on the first day, 2 on the second day, 4 on the third day, 8 mangoes on the fourth day and so on for ten days. Which option should the boy choose to get the maximum number of mangoes?

Find the sum of first n terms of the series

(i) 7 + 77 + 777 + … . (ii) 0.4 + 0.94 + 0.994 + … .

Suppose that five people are ill during the first week of an epidemic and each sick person

spreads the contagious disease to four other people by the end of the second week and so on. By the end of 15th week, how many people will be affected by the epidemic

A geometric series consists of even number of terms. The sum of all terms is 3 times the sum of odd terms. Find the common ratio.

Ans. r = 2

If S₁,S₂and S₃ are the sum of first n, 2n and 3n terms of a geometric series respectively,

then prove that S₁(S₃ – S₂) = (S₂ – S₁)².