Find the constant term in the expansion of `(sqrtx+1/(3x^2))^10`.

Answer

N/a

Explanation

`T_(r+1)=^(10)C_(r)." ("sqrt(x)^(10-r).((1)/(3x^(2)))^(r)`
`=^(10)C_(r).x^((10-r)/(3)).(1)/(3^r.x^(2r))`
`=^(10)C_(r).(1)/(3^(r)).x^((10-r)/(2)-2r)`
`=^(10)C_(r).(1)/(3^r).x^((10-5r)/(2))`
For the term independent of X
`(10-5r)/(2)=0`
`rArr" "r=2`
`:.` term independent of x
`=^(10)C_(2).(1)/(3^2) =(|ul10)/(|ul2|ul8).(1)/(9)=(9xx10)/(1xx2).(1)/(9)=5.`