Question

Tìm số tự nhên x:

1/3 + 1/6 + 1/10 +....+1/x(x+1):2 = 2015/2016

Answer 1

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right):2}=\frac{2015}{2016}\)

\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2016}\)

\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2015}{2016}\)

\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2015}{2016}:2\)

\(\frac{1}{2}-\frac{1}{x+1}=\frac{2015}{4032}\)

\(\frac{1}{x+1}=\frac{1}{2}-\frac{2015}{4032}=\frac{1}{4032}\)

=> x+1=4032

=> x = 4032 - 1

=> x = 4031