InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
`underset(n to oo)lim(1)/(2)" " underset(r=+1)overset(2n)sum (r)/(sqrt(n^(2)+r^(2)))` equalsA. `1+sqrt5`B. `-1+sqrt5`C. `-1+sqrt2`D. `1+sqrt2` |
|
Answer» Correct Answer - B Let `l=underset(nrarroo)(lim)(1)/(n)sum_(r=1)^(2n)(r)/(sqrt(n^(2)-r^(2)))` `=underset(nrarroo)(lim)(1)/(n)sum_(r=1)^(2n)(r)/(sqrt(1+((r)/(n))^(2)))` `=underset(nrarroo)(lim)(1)/(n)sum_(r=1)^(2n)((r)/(n))/(sqrt(1+((r)/(n))^(2)))` Put `(r)/(n)=x,(1)/(n)=dx, underset(nrarroo)(lim)sum_(r=1)^(2n)=int_(0)^(2)` `therefore" "l=int_(0)^(2)(x)/(sqrt(1+x^(2)))dx=[sqrt(1+x^(2))]_(0)^(2)` `=sqrt5-1` |
|