Question

[Mi Mi Mi]

\(\frac{1}{2x4}\)+ \(\frac{1 }{4x6}\)+ \(\frac{1}{6x8}\) + \(\frac{1}{8x10}\)+ ........... + \(\frac{1}{98x100}\) = ?
 

Answer 1

[Lục Minh Hoàng]

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\)

\(=\frac{1}{2}-\frac{1}{100}\)

\(=\frac{50}{100}-\frac{1}{100}=\frac{49}{100}\)

Answer 2

[Đỗ Lê Tú Linh]

1/2*4+1/4*6+1/6*8+1/8*10+...+1/98*100

=1/2*2(1/2*4+1/4*6+1/6*8+1/8*10+...+1/98*100)

=1/2(2/2*4+2/4*6+2/6*8+2/8*10+...2/98*100)

=1/2(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+...+1/98-1/100)

=1/2[(1/2-1/100)+(1/4-1/4)+(1/6-1/6)+...+(1/98-1/98)

=1/2*(1/2-1/100)=1/2*(50/100-1/100)=1/2*49/100=49/200