Question

Tính nhanh:

M= 2/ 3.5 + 2/ 5 .7   +2 /7.9 + ....+  2/97 . 99

GIẢI RA TỪNG  BƯỚC GIÚP MK VỚI.MK SẼ TICK CHO BN NÀO CÓ LỜI GIẢI CHI TIẾT .

Answer 1

\(M=\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{97\cdot99}\)

\(M=\frac{5-3}{3\cdot5}+\frac{7-5}{5\cdot7}+\frac{9-7}{7\cdot9}+...+\frac{99-97}{97\cdot99}\)

\(M=\frac{5}{3\cdot5}-\frac{3}{3\cdot5}+\frac{7}{5\cdot7}-\frac{5}{5\cdot7}+\frac{9}{7\cdot9}-\frac{7}{7\cdot9}+...+\frac{99}{97\cdot99}-\frac{97}{97\cdot99}\)

\(M=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\)

\(M=\frac{1}{3}-\frac{1}{99}\)

\(M=\frac{33}{99}-\frac{1}{99}\)

\(M=\frac{32}{99}\)

Vậy \(M=\frac{32}{99}\)

Answer 2

Có 2/ 3.5 + 2/ 5.7 + 2/ 7.9 +...+ 2/ 97.99

= 1/3 -1/5 +1/5 -1/7 +1/7 -1/9 +...+ 1/ 97- 1/99

= 1/3 - 1/99

= 32/ 99

Answer 3

M=\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{97\cdot99}\)

M=\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\)

M=\(\frac{1}{3}-\frac{1}{99}\)

M=\(\frac{32}{99}\)