Question

tinh tong S , biet : S = \(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+.......+\frac{1}{2010x2011}\)

k mk 3 cai nha mk k lai cho

Answer 1

\(S=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2010.2011}\)

\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2010}-\frac{1}{2011}\)

\(S=1-\frac{1}{2011}\)

\(S=\frac{2010}{2011}\)

Answer 2

Answer 3

Phân tích: 1 / 1 x 2 = 1 - 1/2

1/2.3 = 1/2 - 1/3

. ....Bạn làm tương tự các số còn lại...

Ta được: 1 - 1/2 + 1/2 - 1/3 + ....+1/ 2010 - 1/2011

= 1 - 1/2011

= 2010/2011

Answer 4

\(S=\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{2010\times2011}\)

\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2010}-\frac{1}{2011}\)

\(S=1-\frac{1}{2011}\)

\(S=\frac{2010}{2011}\)

Answer 5

S=1-1/2+1/2-1/3+...+1/2010-1/2011

S=1-1/2011

S=2010/2011