Let S(n)=sum(k=1)^(n)n/(n^(2)+kn+k^(2)) ...

Let `S_(n)=sum_(k=1)^(n)n/(n^(2)+kn+k^(2))` and `T_(n)=sum_(k=0)^(n-1)n/(n^(2)+kn+k^(2))` for `n=1,2,3,`………. Then

A

`S_(n) lt(pi)/(3sqrt3)`

B

`S_(n) gt (pi)/(3sqrt3)`

C

`T_(n) lt (pi)/(3sqrt3)`

D

`T_(n) gt (pi)/(3sqrt3)`

Text Solution

Verified by Experts

The correct Answer is:

D

Topper's Solved these Questions

DEFINITE INTEGRAL
ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|5 Videos
COORDINATE SYSTEM AND COORDINATES
ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos
DETERMINANTS
ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

Let S_n=sum_(k=0)^n n/(n^2+k n+k^2) and T_n=sum_(k=0)^(n-1)n/(n^2+k n+k^2) ,for n=1,2,3,......., then

Let S_n=sum_(k=0)^n n/(n^2+kn+k^2) and T_n=sum_(k=0)^(n-1) n/(n^2+kn+k^2) for n=1,2,3... then (a) S_n lt pi/3sqrt(3) b) S_n gt pi/3sqrt(3) (c) T_n lt pi/3sqrt(3) (d) T_n gt pi/3sqrt(3)

Let T_(n) = sum_(r=1)^(n) (n)/(r^(2)-2r.n+2n^(2)), S_(n) = sum_(r=0)^(n)(n)/(r^(2)-2r.n+2n^(2)) then

The sum S_(n)=sum_(k=0)^(n)(-1)^(k)*^(3n)C_(k) , where n=1,2,…. is

Let S_(n)=sum_(r=1)^(n)((r^(4)_r^(3)n+r^(2)n^(2)+2n^(4))/(n^(5))) and T_(n)=sum_(r=0)^(n-1)((r^(4)+r^(3)n^(2)+2n^(4))/(n^(5))),n=1,2,3, ……….then

T_(n) =sum _( r =2n )^(3n-1) (r)/(r ^(2) +n ^(2)), S_(n) = sum _(r =2n+1)^(3n) (r )/(r ^(2) + n ^(2)), then AA n in {1,2,3...}:

If S_(r)= sum_(r=1)^(n)T_(1)=n(n+1)(n+2)(n+3) then sum_(r=1)^(10) 1/(T_(r)) is equal to

Evaluate ("lim")_(n rarr oo)sum_(k=1)^nk/(n^2+k^2)

If S_(n) = sum_(n=1)^(n) (2n + 1)/(n^(4) + 2n^(3) + n^(2)) then S_(10) is less then

Prove that sum_(k=0)^(n) (-1)^(k).""^(3n)C_(k) = (-1)^(n). ""^(3n-1)C_(n)

ARIHANT MATHS ENGLISH-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)

For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...
Text Solution
|
Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...
Text Solution
|
Which of the following is true?
Text Solution
|
For any real number x ,l e t[x] denote the largest integer less than o...
Text Solution
|
Let f be a non-negative function defined on the interval [0,1]. If int...
Text Solution
|
If int(n)=int(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,………. then
Text Solution
|
Let S(n)=sum(k=1)^(n)n/(n^(2)+kn+k^(2)) and T(n)=sum(k=0)^(n-1)n/(n^(2...
Text Solution
|
Then integral int(pi//4)^((3pi)/4) (dx)/(1+cosx) is equal to
Text Solution
|
"Let " I(n)=int tan^(n)x dx,(n gt 1). I(4)+I(6)=a tan^(5)x+bx^(5)+C, "...
Text Solution
|
lim(n -> oo) (((n+1)(n+2)(n+3).......2n) / n^(2n))^(1/n)is equal to
Text Solution
|
The integral int(2)^(4)(logx^(2))/(logx^(2)+log(36-12x+x^(2))) dx is e...
Text Solution
|
The integral int(0)^(pi)sqrt(1+4"sin"^(2)x/2-4"sin"x/2)dx is equals to...
Text Solution
|
Statement I The value of the integral int(pi//6)^(pi//3) (dx)/(1+sqrt...
Text Solution
|
The intercepts on x- axis made by tangents to the curve, y=int(0)^(x)|...
Text Solution
|
If g(x)=int(0)^(x)cos^(4)t dt, then g(x+pi) equals to (a)(g(x))/(g(pi)...
Text Solution
|
The value of int(0)^(1)(8log(1+x))/(1+x^(2))dx is
Text Solution
|
For x epsilon(0,(5pi)/2), definite f(x)=int(0)^(x)sqrt(t) sin t dt. T...
Text Solution
|
Let p(x) be a function defined on R such that lim(xrarr infty) f (3x...
Text Solution
|
int(0)^(pi)[cos x] dx, [ ] denotes the greatest integer function , is ...
Text Solution
|
Let I=int(0)^(1)(sinx)/(sqrtx) dx and f= int(0)^(1)( cos x)/(sqrtx) dx...
Text Solution
|