IIMB 2001 (QA) PYQs

Goku starts receiving an annual stipend of Rs. $100$. Each subsequent year, his stipend is reduced to $90\%$ of the amount he received the previous year. Calculate the maximum total amount Goku will receive over an infinite period.

Solve:

$\dfrac{1}{1\times2\times3\times4}+\dfrac{1}{2\times3\times4\times5}+\dfrac{1}{3\times4\times5\times6}+\cdots+\dfrac{1}{15\times16\times17\times18}$

Find the sum of the series $14,11,8,5, \ldots,-82$ such that only the odd terms are considered: