\(\frac{2}{8}+\frac{2}{24}+\frac{2}{48}+...+\frac{2}{40400}\)
\(=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{200.202}\)
\(=\frac{4-2}{2.4}+\frac{6-4}{4.6}+\frac{8-6}{6.8}+...+\frac{202-200}{200.202}\)
\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{200}-\frac{1}{202}\)
\(=\frac{1}{2}-\frac{1}{202}\)
\(=\frac{50}{101}\)
A = 2/2*4+2/4*6+2/6*8+...+2/200*202
=1/2-1/4+1/4-1/6+1/6-1/8+...+1/200-1/202
=1/2-1/202
=50/101
Đặt A=2/8+2/24+2/48+..+2/40400
Ta có:A=2/8+2/24+2/48+2/40400
=>A=2/2.4+2/4.6+2/6.8+..+2/200.202
=>A=1/2-1/4+1/4-1/6+1/6-1/8+..+1/200-1/202
=>A=1/2-1/202
=>A=100/202=50/101
Vậy A=50/101
Ta đặt tên cho biểu thức trên là A
\(\Rightarrow A=\frac{2}{8}+\frac{2}{24}+\frac{2}{48}+...+\frac{2}{40400}\)
\(A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{200.202}\)
\(A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{200}-\frac{1}{202}\)
\(A=\frac{1}{2}-\frac{1}{202}\)
\(A=\frac{50}{101}\)
Vậy\(A=\frac{50}{101}\)
\(\frac{2}{8}+\frac{2}{24}+\frac{2}{48}+...+\frac{2}{40400}\)
\(=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{200.202}\)
\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{200}-\frac{1}{202}\)
\(=\frac{1}{2}-\frac{1}{202}=\frac{101}{202}-\frac{1}{202}=\frac{100}{202}=\frac{50}{101}\)
