Question

[Lại Nguyễn Gia Hân]

Tính

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

b) \(N=\frac{3}{5\times7}+\frac{3}{7\times9}+\frac{3}{9\times11}+...+\frac{3}{197\times199}\)

Các bạn giúp mk nha! Cần lắm! Thanks các bạn nhiều

Answer 1

[Võ Vân Khánh]

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

    m = 1/3-1/99=32/99

   Sorry chị em ko làm đc câu b vì em mới học lớp 4

   k em ha

Answer 2

[nguyen van huy]

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

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

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

\(\Rightarrow M=\frac{33}{99}-\frac{1}{99}=\frac{32}{99}\)

b)  \(N=\frac{3}{5\times7}+\frac{3}{7\times9}+\frac{3}{9\times11}+...+\frac{3}{197\times199}\)

\(\Rightarrow N=3\times\left(\frac{1}{5\times7}+\frac{1}{7\times9}+\frac{1}{9\times11}+...+\frac{1}{197\times199}\right)\)

\(\Rightarrow N=3\times\left[2\times\left(\frac{1}{5\times7}+\frac{1}{7\times9}+\frac{1}{9\times11}+...+\frac{1}{197\times199}\right)\right]\)

\(\Rightarrow N=3\times\left(\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}+...+\frac{2}{197\times199}\right)\)

\(\Rightarrow N=3\times\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{197}-\frac{1}{199}\right)\)

\(\Rightarrow N=3\times\left(\frac{1}{5}-\frac{1}{199}\right)\)

\(\Rightarrow N=3\times\frac{194}{995}=\frac{582}{995}\)

----Chúc em học giỏi !----