Question

4/8x9+4/9x10+4/10x11+.....+4/66x67

help me 

Answer 1

A = \(\dfrac{4}{8\times9}\)+\(\dfrac{4}{9\times10}\)+\(\dfrac{4}{10\times11}\)+...+\(\dfrac{4}{66\times67}\)

A = 4 \(\times\)( \(\dfrac{1}{8\times9}\)+\(\dfrac{1}{9\times10}\)+\(\dfrac{1}{10\times11}\)+...+\(\dfrac{1}{66\times67}\))

A = 4\(\times\)(\(\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}+\)...+\(\dfrac{1}{66}-\dfrac{1}{67}\))

A = 4\(\times\)(\(\dfrac{1}{8}\) - \(\dfrac{1}{67}\))

A = 4 \(\times\) \(\dfrac{59}{536}\)

A = \(\dfrac{59}{134}\)

A =