Question

A1= 1/1x2x3 + 1/2x3x4 + 1/3x4x5 +......+ 1/37x38x39

A1=?

Answer 1

A = \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{37.38.39}\)

= \(\frac{1}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{37.38.39}\right)\)

= \(\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{37.38}-\frac{1}{38.39}\right)\)

= \(\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{38.39}\right)\)

= \(\frac{1}{2}\left(\frac{1}{2}-\frac{1}{1482}\right)\)

= \(\frac{1}{2}.\frac{390}{781}=\frac{195}{781}\)

Answer 2

=195/781

Answer 3

= 40 / 39