Home
Class 12
MATHS
Evaluate lim(nrarroo)(2)/(n)(sin.(pi)/...

Evaluate
`lim_(nrarroo)(2)/(n)(sin.(pi)/(2n)+sin.(2pi)/(2n)+sin.(3pi)/(2n)+....+sin.(npi)/(2n))`

Text Solution

Verified by Experts

The correct Answer is:
`(4)/(pi)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    FIITJEE|Exercise EXERCISE 2:|3 Videos
  • DEFINITE INTEGRAL

    FIITJEE|Exercise EXERCISE 3:|5 Videos
  • DEFINITE INTEGRAL

    FIITJEE|Exercise SOLVED PROBLEMS (OBJECTIVE)|29 Videos
  • COMPLEX NUMBER

    FIITJEE|Exercise NUMERICAL BASED|3 Videos
  • DETERMINANT

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

Evaluate lim_(ntooo)(1)/(n)[sin^(2k).(pi)/(2n)+sin^(2k).(2pi)/(2n)+....+sin^(2k).(pi)/(2)]

Evaluate: (lim_(n rarr oo)n cos((pi)/(4n))sin((pi)/(4n))

lim_( n to oo) (sin ""(pi)/(2n) . sin ""(2pi)/(2n). sin ""(3pi)/(2n)......sin""((n -1) pi)/(2n))^(1//n) is equal to

lim_(n rarr oo)n sin\ (2 pi)/(3n)*cos\ (2 pi)/(3n)

The value of lim_(n rarr oo)(1)/(n^(2)){(sin^(3)pi)/(4n)+2(sin^(3)(2 pi))/(4n)+...+n(sin^(3)(n pi))/(4n)} is equal to

Compute underset(n rarr oo)("lim")(pi)/(n)| "sin"(pi)/(n) + "sin"(2pi)/(n)+ ….+ "sin"((n-1)pi)/(n)|

The value of lim_( n to oo) (1)/(n) ( sin (pi/ n) + sin (2pi/n) + …+ sin (n pi/ n) ) is

Evaluate: lim_(x rarr oo)sin^(n)((2 pi n)/(3n+1)),n in N

Evaluate sin((pi)/(n))+sin((3 pi)/(n))+sin((5 pi)/(n))+ to n terms.

Let 1, z_(1),z_(2),z_(3),…., z_(n-1) be the nth roots of unity. Then prove that (1-z_(1))(1 - z_(2)) …. (1-z_(n-1))= n . Also,deduce that sin .(pi)/(n) sin.(2pi)/(pi)sin.(3pi)/(n)...sin.((n-1)pi)/(n) = (pi)/(2^(n-1))