Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
S=\(\frac{2}{5.7}\)+\(\frac{2}{7.9}\)+....+\(\frac{2}{93.95}\)+\(\frac{3}{95.98}\)+\(\frac{4}{98.102}\)+\(\frac{5}{102.107}\)+\(\frac{2012}{107.2119}\)
S=\(\frac{1}{5}\)-\(\frac{1}{7}\)+\(\frac{1}{7}\)-\(\frac{1}{9}\)+....+\(\frac{1}{93}\)-\(\frac{1}{95}\)+\(\frac{1}{95}\)-\(\frac{1}{98}\)+\(\frac{1}{98}\)-\(\frac{1}{102}\)+\(\frac{1}{102}\)-\(\frac{1}{107}\)+\(\frac{1}{107}\)-\(\frac{1}{2119}\)
S=\(\frac{1}{5}\)-\(\frac{1}{2119}\)
S=\(\frac{2114}{10595}\)
\(S=\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}+..............+\frac{2}{93\cdot95}\)
\(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+............+\frac{1}{93}-\frac{1}{95}\)
\(=\frac{1}{5}-\frac{1}{95}\)
S = 2/5.7+ 2/7.9+...+2/93.95
=1/5-1/7+1/7-1/9+1/11+...+1/93+1/95
=1/5-1/95
=19/95-1/95
=18/95
Đặt \(A=\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{x\left(x+2\right)}\)(sửa đề)
\(\Rightarrow A=\frac{1}{2}.3.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)\)
\(\Rightarrow A=\frac{3}{2}\left(\frac{1}{3}-\frac{1}{x+2}\right)\)
\(\Rightarrow A=\frac{1}{2}-\frac{3}{2x+4}\)
4/3.5+4/5.7+4/7.9+4/9.11
=4.(1/3.5+1/5.7+1/7.9+1/9.11)
=4.1/2.(2/3.5+2/5.7+2/7.9+2/9.11)
=2.(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=2.(1/3-1/11)
=2.8/33
=16/33
4/3.5+4/5.7+4/7.9+4/9.11
=4.2/2.3.5+4.2/2.5.7+4.2/2.7.9+4.2/2.9.11
=4/2.2/3.5+4/2.2/5.7+4/2.2/7.9+4/2.2/9.11
=4/2.(2/3.5+2/5.7+2/7.9+2/9.11)
=4/2.(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=2.(1/3-1/11)
=2.8/33
=16/33
giúp tui viết cả lời giải nữa tui sắp nộp zùi ai trả lời đúng tui k 3 cái cho
\(B=\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)
\(=\frac{1}{3}-\frac{1}{11}=\frac{11}{33}-\frac{3}{33}=\frac{8}{33}\)
Khoảng cách có rồi thì bạn áp dụng công thức : \(\frac{a}{m.n}=\frac{1}{m}-\frac{1}{n}\)(với n-m=a) là làm được
S=\(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{93.95}+\frac{3}{95.98}+\frac{4}{98.102}+\frac{5}{102.17}+\frac{2012}{107..2119}\)
S=\(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{93}-\frac{1}{95}+\frac{1}{95}-\frac{1}{98}+\frac{1}{98}-\frac{1}{102}+\frac{1}{102}-\frac{1}{107}+\frac{1}{107}-\frac{1}{2119}\)
S=\(\frac{1}{5}-\frac{1}{2119}\)
S=\(\frac{2114}{10595}\)