Question

A=\(\frac{2}{3\cdot1}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{99\cdot101}\)

lam ho minh voi

Answer 1

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

\(A=\frac{2}{3}+\left(\frac{1}{3}-\frac{1}{101}\right)\)

\(A=\frac{2}{3}+\frac{98}{303}\)

\(A=\frac{100}{101}\)

Answer 2

\(A=\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+.....+\frac{2}{99x101}\)

\(A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{99}-\frac{1}{100}=\)

\(A=\frac{1}{1}-\frac{1}{100}\)

\(A=\frac{99}{100}\)

Answer 3

A=2/1*3+2/3*5+2/5*7+....+2/99*101

A=1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101

A=1-1/101

A=100/101

Answer 4

bui cuoc duy sai roi

Answer 5

\(A=\frac{2}{3x1}+\frac{2}{3x5}+.....+\frac{2}{99x101}\)

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

\(A=\frac{2}{3}+\left(\frac{2}{3}-\frac{1}{101}\right)\)

\(A=\frac{100}{101}\)

Answer 6

\(A=\frac{2}{3x1}+\frac{2}{3x5}+.....+\frac{2}{99x101}\)

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

\(A=\frac{2}{3}+\left(\frac{2}{3}-\frac{1}{101}\right)\)

\(A=\frac{100}{101}\)

Answer 7

\(A=\frac{2}{3x1}+\frac{2}{3x5}+.....+\frac{2}{99x101}\)

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

\(A=\frac{2}{3}+\left(\frac{2}{3}-\frac{1}{101}\right)\)

\(A=\frac{100}{101}\)

Answer 8

\(A=\frac{2}{3x1}+\frac{2}{3x5}+.....+\frac{2}{99x101}\)

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

\(A=\frac{2}{3}+\left(\frac{2}{3}-\frac{1}{101}\right)\)

\(A=\frac{100}{101}\)

Answer 9

\(A=\frac{2}{3x1}+\frac{2}{3x5}+.....+\frac{2}{99x101}\)

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

\(A=\frac{2}{3}+\left(\frac{2}{3}-\frac{1}{101}\right)\)

\(A=\frac{100}{101}\)

Answer 10

A =2/1.3+2/3.5+1/5.7+..........+2/99.101

A =1-1/3 + 1/3-1/5+ 1/5-1/7+........+1/99-1/101

A =1-1/101

A=100/101

VẬY A =100/101