Question

m=2/3*5+2/5*7+2/7*9+....+2/97*99

Answer 1

\(\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+.....+\frac{2}{97\times99}\)

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

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

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

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

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Answer 2

M=2/3.5+2/5.7+...+2/97.99

M=1.(1/3-1/5+...+1/97-1/99)

M=1.(1/3-1/99)

M=32/99

Answer 3

M=2/3*5+2/5*7+2/7*9+...+2/97*99

2/3*5=5-3/3*5=5/3*5-3/3*5=1/3-1/5

2/5*7=7-5/5*7=7/5*7-5/5*7=1/5-1/7

2/7*9=9-7/7*9=9/7*9-7/7*9=1/7-1/9

......

2/97*99=99-97/97*99=99/97*99-97/97*99=1/97-1/99

M=1/3-1/5+1/5-1/7+1/7-1/9+....+1/97-1/99= 1/3-1/99= 32/99