Home
Class 12
MATHS
Evaluate lim(ntooo) (1^(3)+2^(3)+3^(3)+....

Evaluate `lim_(ntooo) (1^(3)+2^(3)+3^(3)+...+n^(3))/(sqrt(4n^(8)+1)).`

Text Solution

Verified by Experts

`underset(ntooo)lim(1^(3)+2^(3)+3^(3)+...+n^(3))/(sqrt(4n^(8)+1))=1/4underset(ntooo)lim(n^(2)(n+1)^(2))/(sqrt(4n^(8)+1))`
`=1/4underset(ntooo)lim(n^(2))/((1)/(n^(4))sqrt(4n^(8)+1))`
`=1/4underset(ntooo)lim(1+(1)/(n))^(2)/(sqrt(4+(1)/(n^(8))))=1/8`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE ENGLISH|Exercise Solved Examples|15 Videos

  • LIMITS

    CENGAGE ENGLISH|Exercise EXERCISE 2.1|10 Videos

  • JEE 2019

    CENGAGE ENGLISH|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE ENGLISH|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Evaluate lim_(ntooo) (4^(n)+5^(n))^(1//n)

The value of lim_(nto oo)(1^(3)+2^(3)+3^(3)+……..+n^(3))/((n^(2)+1)^(2))

Evaluate lim _( x to oo) ((1^(2) )/(n ^(3) +1 ^(3))+(2 ^(2))/(n ^(3) +2 ^(3)) + (3 ^(2))/(n ^(3)+ 3 ^(3))+ .... + (4)/(9n)).

Evaluate lim_(ntooo) (1)/(1+n^(2))+(2)/(2+n^(2))+...+(n)/(n+n^(2)).

Evaluate lim_(ntooo) sin^(n)((2pin)/(3n+1)),ninN.

Evaluate lim_(ntooo) ((1^(2)-2^(2)+3^(2)-4^(2)+5^(2)+...n" terms"))/(n^(2)).

Evaluate lim_(ntooo) n^(-n^(2))[(n+2^(0))(n+2^(-1))(n+2^(-2))...(n+2^(-n+1))]^(n) .

If L= lim_(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((n^(2)+1))) , then the value of L^(4) is _____________. (a) -1/4 (b) 1/2 (c) 1 (d) none of the above

The value of lim_(n to oo)((1)/(1^(3)+n^(3))+(2^(2))/(2^(3)+n^(3))+..........+(n^(2))/(n^(3)+n^(3))) is :

Evaluate lim_(ntooo) (n^(p)sin^(2)(n!))/(n+1),"wher "0ltplt1.