Question

A = \(\dfrac{55}{11x16}\)+ \(\dfrac{55}{16x21}\)+\(\dfrac{55}{21x26}\)+\(\dfrac{55}{26x31}\)+\(\dfrac{55}{31x36}\)+\(\dfrac{55}{36x41}\)

Answer 1

`A = 55/( 11xx16 ) + 55/( 16xx21 ) + 55/( 21xx26 ) + 55/( 26xx31) + 55/( 31xx36)+55/(36xx41)`

`A = 11 xx ( 5/( 11xx16 ) + 5/( 16xx21 ) + 5/( 21xx26 ) + 5/( 26xx31) + 5/( 31xx36)+5/(36xx41)`

`A = 11 xx ( 1/11 - 1/16 + 1/16 - 1/21 + 1/21 - 1/26 + 1/26 - 1/31 + 1/31 - 1/36 + 1/36 - 1/41 )`

`A = 11 xx ( 1/11 - 1/41 )`

`A = 1 - 11/41`

`A = 30/41` 

Answer 2

\(A=55.\left(\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{31}+\dfrac{1}{31}-\dfrac{1}{36}+\dfrac{1}{36}-\dfrac{1}{41}\right)\)

\(A=55\times\left(\dfrac{1}{11}-\dfrac{1}{41}\right)=55\times\dfrac{30}{451}=\dfrac{150}{41}\)