Question

15/4+15/28+15/70+..+15/x+(x+3)=99/20

Answer 1

\(\frac{15}{4}+\frac{15}{28}+\frac{15}{70}+...+\frac{15}{x.\left(x+3\right)}=\frac{99}{20}\)

=> \(5.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{x.\left(x+3\right)}\right)=\frac{99}{20}\)

=> \(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{x}-\frac{1}{x+3}=\frac{99}{20}:5\)

=> \(1-\frac{1}{x+3}=\frac{99}{20}.\frac{1}{5}=\frac{99}{100}\)

=> \(\frac{1}{x+3}=1-\frac{99}{100}\)

=> \(\frac{1}{x+3}=\frac{1}{100}\)

=> x + 3 = 100

=> x = 100 - 3

=> x = 97