Question

[Thanh Ngọc Huỳnh]

Cho S=1/1x3+1/3x5+1/5x7+..................1/99x101

Khi đó 2S+ 1/101=...................

M

Answer 1

[toan bai kho]

ta có : 2S=\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)

          2S=\(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)

          2S=\(\frac{1}{1}-\frac{1}{101}\)

      2S+\(\frac{1}{101}\)= \(\frac{1}{1}-\frac{1}{101}+\frac{1}{101}\)

      2S+\(\frac{1}{101}\)=1

ok