Question

a) Tìm số nguyên dương x :

    (x-3)+(x-2)+(x-1)+...+9+10+2011=2011

b) Tìm số tự nhiên x : 
     \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{n\left(n+1\right)}\)

Answer 1

Ta có : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+......+\frac{2}{n\left(n+1\right)}\)

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

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

\(=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+......+\frac{1}{n\left(n+1\right)}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{n}-\frac{1}{n+1}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{n+1}\right)\)

\(=1-\frac{2}{n+1}\)

\(=\frac{n+1}{n+1}-\frac{2}{n+1}\)

\(=\frac{n-1}{n+1}\)

Answer 2

bài 2 x đâu vậy bn