Question

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

Tính bằng cách thuận tiện.   Giúp mình nha !!!!!!!!!

Answer 1

\(A=\frac{7}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+.......+\frac{2}{99.101}\right)\)

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

\(=\frac{7}{2}.\left(1-\frac{1}{101}\right)\)

\(=\frac{7}{2}.\frac{100}{101}\)

\(=\frac{350}{101}\)

Answer 2

\(A=\frac{7}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+.....+\frac{2}{99.101}\right)\)

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

\(=\frac{7}{2}.\left(1-\frac{1}{101}\right)\)

\(=\frac{7}{2}.\frac{100}{101}\)

\(=\frac{350}{101}\)

Answer 3

\(A=\frac{7}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+.....+\frac{2}{99.101}\right)\)

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

\(=\frac{7}{2}.\left(1-\frac{1}{101}\right)\)

\(=\frac{7}{2}.\frac{100}{101}\)

\(=\frac{350}{101}\)