lim(nrarroo) [(1)/(n)+(sqrt(n^(2)-1^(2))...

`lim_(nrarroo) [(1)/(n)+(sqrt(n^(2)-1^(2)))/(n^(2))+(sqrt(n^(2)-2^(2)))/(n^(2))+...+(sqrt(n^(2)-(n-1)^(2)))/(n^(2))]`

Text Solution

Verified by Experts

The correct Answer is:

`(pi)/(4)`

Topper's Solved these Questions

DEFINITE INTEGRAL
CHHAYA PUBLICATION|Exercise EXERCISE 9B ( MULTIPLE CHOICE TYPE QUESTIONS )|6 Videos
DEFINITE INTEGRAL
CHHAYA PUBLICATION|Exercise EXERCISE 9B (VERY SHORT ANSWER TYPE QUESTIONS)|20 Videos
DEFINITE INTEGRAL
CHHAYA PUBLICATION|Exercise SHORT ANSWER TYPE QUESTIONS|61 Videos
COORDINATE GEOMETRY
CHHAYA PUBLICATION|Exercise JEE Advanced Archive (2016)|3 Videos
DEFINITE INTEGRAL AS AN AREA
CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

lim_(n to oo)[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt(n^(2)-3^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))]

lim_(nrarroo) {(1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))} is equal to-

Find the value of underset(ntooo)lim[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt(n^(2)-3^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))]

lim_(nrarroo) [(1)/(n)+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+...+(1)/(8n)]

lim_(nrarroo)[(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+(n+3)/(n^(2)+3^(2))+...+(1)/(n)]

Evaluate : lim_(nrarroo)[(1+(1)/(n^(2)))^((2)/(n^(2)))(1+(2^(2))/n^(2))^((4)/(n^(2)))(1+(3^(2))/(n^(2)))^((6)/(n^(2)))...(1+(n^(2))/(n^(2)))^((2n)/(n^(2)))]

lim_(nrarroo) [(1)/(n)+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+...+(1)/(8n)] is equal to

lim_(nrarroo)[(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+(n)/(n^(2)+3^(2))+...+(n)/(n^(2)+n^(2))]

Evaluate : underset(nrarrinfty)Lt[(1)/(sqrt(n^2 - 1^2)) + 1/(sqrt(n^2-2^2)) +1/(sqrt(n^2 - 3^2))+....+ 1/(sqrt(n^2 - (n-1)^2))]

lim_(nrarroo) [(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)/(n)]

CHHAYA PUBLICATION-DEFINITE INTEGRAL -LONG ANSWER TYPE QUESTIONS

int(0)^((3pi)/(4))(sinxdx)/(1+cos^(2)x)=(pi)/(4)+tan^(-1)((1)/(sqrt(2)...
Text Solution
|
int(0)^((pi)/(2))sin 2x tan^(-1)(sinx)dx
Text Solution
|
int(0)^((pi)/(4))xcosxcos3xdx=(pi+2)/(16)
Text Solution
|
If f(x) is periodic function of period t show that int(a)^(a+t)f(x)dx ...
Text Solution
|
If y=int(0)^(x)(t-1)(t-2)^(2)dt, find x for which (dy)/(dx)=0.
Text Solution
|
If int(0)^(y)e^(t)dt+int(0)^(x)cost^(2)dt=0 show that, e^(y)(dy)/(dx)+...
Text Solution
|
lim(n to oo)(1^(9)+2^(9)+3^(9)+...+n^(9))/(n^(10))
Text Solution
|
lim(nrarroo) [(1)/(n+1)+(1)/(n+2)+(1)/(n+3)+...+(1)/(n+n)]
Text Solution
|
lim(nrarroo) [(1)/(n)+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+...+(1)/...
Text Solution
|
lim(nrarroo)[(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+(n)/(n^(2)+3^(2))+......
Text Solution
|
lim(nrarroo) [(1^(2))/(n^(3)+1^(3))+(2^(2))/(n^(3)+2^(3))+(3^(2))/(n^(...
Text Solution
|
lim(nrarroo)[(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+(n+3)/(n^(2)+3^(2...
Text Solution
|
lim(nto oo)[(sqrt(n+1)+sqrt(n+2)+...+sqrt(2)n)/(sqrt(n^(3)))]
Text Solution
|
lim(n to oo)[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt...
Text Solution
|
lim(nrarroo) [(1)/(n)+(sqrt(n^(2)-1^(2)))/(n^(2))+(sqrt(n^(2)-2^(2)))/...
Text Solution
|
lim(nrarroo) [(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)/(n)]
Text Solution
|
Show that, int(0)^(1)(1)/(x)log(1+x)dx=1-(1)/(2^(2))+(1)/(3^(2))-(1)/(...
Text Solution
|
If I(m)=int(1)^(e)(logx)^(m)dx, show that, I(m)+mI(m-1)lt3.
Text Solution
|
If u(n)=int(0)^((pi)/(4))tan^(n)xdx, show that, u(n)+u(n-2)=(1)/(n-1)(...
Text Solution
|
If u(n)=int(0)^((pi)/(2))(sin(2n-1)x)/(sinx)dxandv(n)=int(0)^((pi)/(2)...
Text Solution
|