Question

\(c=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+.....+\frac{1}{98.100}\)

 

Answer 1

=1/2-1/4+1/4-1/6+....+1/98-1/100

=1/2-1/100

=49/100

Answer 2

=1/2-1/4+1/4-1/6+ ... +1/98-1/100

=1/2-1/100

=49/100

Answer 3

C= \(\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+....+\frac{2}{98.100}\right)\)

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

  = \(\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{100}\right)\)

  = \(\frac{1}{2}.\left(\frac{50}{100}-\frac{1}{100}\right)\)

  = \(\frac{1}{2}.\frac{49}{100}\)

  = \(\frac{49}{200}\)