\(a,A=\frac{1}{25\cdot27}+\frac{1}{27\cdot29}+...+\frac{1}{73\cdot75}\)
\(A=\frac{1}{2}\left[\frac{2}{25\cdot27}+\frac{2}{27\cdot29}+...+\frac{2}{73\cdot75}\right]\)
\(A=\frac{1}{2}\left[\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\right]\)
\(A=\frac{1}{2}\left[\frac{1}{25}-\frac{1}{75}\right]=\frac{1}{2}\cdot\frac{2}{75}=\frac{1}{75}\)
\(b,B=\frac{1}{8\cdot11}+\frac{1}{11\cdot14}+\frac{1}{14\cdot17}+...+\frac{1}{197\cdot200}\)
\(3B=\frac{3}{8\cdot11}+\frac{3}{11\cdot14}+\frac{3}{14\cdot17}+...+\frac{3}{197\cdot200}\)
\(3B=\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{197}-\frac{1}{200}\)
\(3B=\frac{1}{8}-\frac{1}{200}\)
\(3B=\frac{3}{25}\)
\(B=\frac{3}{25}:3=\frac{1}{25}\)
#)Giải :
a, \(A=\frac{1}{25.27}+\frac{1}{27.29}+...+\frac{1}{73.75}\)
\(A=\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\)
\(A=\frac{1}{25}-\frac{1}{75}\)
\(A=\frac{2}{75}\)
b, \(B=\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+...+\frac{1}{197.200}\)
\(B=\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+...+\frac{1}{197}-\frac{1}{200}\)
\(B=\frac{1}{8}-\frac{1}{200}\)
\(B=\frac{3}{25}\)
#~Will~be~Pens~#
\(A=\frac{1}{25.27}+\frac{1}{27.29}+...+\frac{1}{73.75}\)
\(2A=\frac{2}{25.27}+\frac{2}{27.29}+...+\frac{2}{73.75}\)
\(2A=\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\)
\(2A=\frac{1}{25}-\frac{1}{75}\)
\(2A=\frac{2}{75}\)
\(A=\frac{2}{75}:2=\frac{1}{75}\)
\(B=\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+...+\frac{1}{197.200}\)
\(3B=\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+...+\frac{3}{197.200}\)
\(3B=\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+...+\frac{1}{197}-\frac{1}{200}\)
\(3B=\frac{1}{8}-\frac{1}{200}\)
\(3B=\frac{3}{25}\)
\(B=\frac{3}{25}:3=\frac{1}{25}\)
#)Ui chết sorry bn, mk ghi thiếu nhé @@
ph là 2A và 3B ms đúng :v
Mấy bn kia lm đúng rùi !
a) \(2A=\frac{2}{25.27}+\frac{2}{27.29}+...+\frac{2}{73.75}=\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\)
\(\Leftrightarrow2A=\frac{1}{25}-\frac{1}{75}=\frac{2}{75}\Rightarrow A=\frac{1}{75}.\)
b)\(3B=\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+...+\frac{3}{197.200}=\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{197}-\frac{1}{200}\)
\(\Leftrightarrow3B=\frac{1}{8}-\frac{1}{200}=\frac{3}{25}\Leftrightarrow B=\frac{1}{25}.\)
A = \(\frac{1}{25.27}+\frac{1}{27.29}+...+\)\(\frac{1}{73.75}\)
2A = \(\frac{2}{25.27}+\frac{2}{27.29}+...+\frac{2}{73.75}\)
2A = \(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\)
2A = \(\frac{1}{25}-\frac{1}{75}\)
2A = \(\frac{3}{75}-\frac{1}{75}\)
=>A = \(\frac{2}{75}:2\)=\(\frac{2}{75}.\frac{1}{2}\)
=> A =\(\frac{1}{75}\)
B = \(\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+...+\frac{1}{197.200}\)
3B = \(\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+...+\frac{3}{197.200}\)
3B = \(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+...+\frac{1}{197}-\frac{1}{200}\)
3B = \(\frac{1}{8}-\frac{1}{200}\)
=> 3B = \(\frac{25}{200}-\frac{1}{200}\)
=> B = \(\frac{24}{200}.\frac{1}{3}\)
=> B = \(\frac{1}{25}\)
#Học'Tốt#
\(A=\frac{1}{25.27}+\frac{1}{27.29}+...+\frac{1}{73.75}\)
\(2A=\frac{2}{25.27}+\frac{2}{27.29}+...+\frac{2}{73.75}\)
\(2A=\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\)
\(2A=\frac{1}{25}+\left(\frac{1}{27}-\frac{1}{27}\right)+\left(\frac{1}{29}-\frac{1}{29}\right)+...+\left(\frac{1}{73}-\frac{1}{73}\right)-\frac{1}{75}\)
\(2A=\frac{1}{25}-\frac{1}{75}\)
\(2A=\frac{2}{75}\)
\(A=\frac{2}{75}:2\)
\(A=\frac{1}{75}\)
~ Hok tốt ~
\(B=\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+...+\frac{1}{197.200}\)
\(3B=\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+...+\frac{3}{197.200}\)
\(3B=\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+...+\frac{1}{197}-\frac{1}{200}\)
\(3B=\frac{1}{8}+\left(\frac{1}{11}-\frac{1}{11}\right)+\left(\frac{1}{14}-\frac{1}{14}\right)+...+\left(\frac{1}{197}-\frac{1}{197}\right)-\frac{1}{200}\)
\(3B=\frac{1}{8}-\frac{1}{200}\)
\(3B=\frac{3}{25}\)
\(B=\frac{3}{25}:3\)
\(B=\frac{1}{25}\)
~ Hok tốt ~