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
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 !----
a M=1/3-1/5+1/5-1/7+1/7-1/9+....+1/97-1/99
M=1/3-1/99
M= 33/99-1/99
M=32/99
b
N=3/2( 2/5x7+2/7x9+2/9x11+...+ 2/ 197x199)
N=3/2x(1/5-1/7+1/7-1/9+1/9-1/11+.....+ 1/197-1/199)
N=3/2x( 1/5-1/199)
N=3/2x194/995
N=291/995
chắc chắn đúng 100% nha bạn
M=\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{97.99}\)
=\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\)
=\(\frac{1}{3}-\frac{1}{99}=\frac{33}{99}-\frac{1}{99}=\frac{32}{99}\)
M = 1/3 - 1/5 + 1/5 - 1/7 + ....... + 1/97 - 1/ 99
M = 1/3 - 1/99
M = 33/99 - 1/99
M = 32/99
