Grades 11-12 Video Solutions 2021-video 2021 11-12/23

Video Transcription

Video Summary

The problem involves determining the value of a sum using a function \( f(x) \) defined by two equations: \( f(x+y) = f(x)f(y) \) and \( f(1) = 2 \). To solve it, we evaluate \( f(n) = 2^n \) by applying the given properties. The sum in question is \( \sum_{n=1}^{2020} \frac{f(n+1)}{f(n)} \). Substituting \( f(n) = 2^n \) results in each term simplifying to 2, making the sum equal to \( 2 \times 2020 = 4040 \). Thus, the final answer is 4040.

Keywords

functional equation

sum evaluation

exponential function

mathematical solution

series simplification