The sum `(7)/(2^2xx5^2)+13/(5^2xx8^2)+19/(8^2xx11^2)+…10` terms is S, then the value of 1024(S) is __________.

Answer

85

Explanation

`S=7/(2^(2)xx5^(2))+13/(5^(2)xx8^(2))+19/(8^(2)xx11^(2))+….10` terms
`=sum_(r=1)^(10)(6r+1)/((3r-1)^(2)(3r+2)^(2))` ltbr gt`=1/3sum_(r=1)^(10)((3r+2)^(2)-(3r-1)^(2))/((3r-1)^(2)(3r+2)^(2))`
`=1/3sum_(r=1)^(10)(1/((3r-1)^(2))-1/((3r+2)^(2)))`
`=1/3(1/2^(2)-1/2^(10))`
`1/3((2^(8)-1)/2^(10))`
`=85/1024`