Home
Class 12
MATHS
Show tha , lim(ntooo) ((1)/( n +1)+(1)/...

Show tha , `lim_(ntooo) ((1)/( n +1)+(1)/( n +2)+ . . . +(1)/( 6 n))= log 6`.

Text Solution

Verified by Experts

`underset(ntooo)(lim) ((1)/(n+1)+(1)/(n+2)+. . . + (1)/(6n))=sum _(r=1)^(5n)(1)/(n+r)`
`=underset(n tooo)(lim) (1)/(n)sum_(r=1)^(5n)(1)/((1+(r)/(n)))`
`=int_(0)^(5)(dx)/(1+x)=[log(1+x)]_(0)^(5)=log6 - log1=6`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    IIT JEE PREVIOUS YEAR|Exercise ESTIMATION, GAMMA FUNCTION AND DERIVATIVE OF INDEFINITE INTEGRAL|22 Videos

  • COMPLEX NUMBERS

    IIT JEE PREVIOUS YEAR|Exercise TOPIC 5 DE-MOIVRES THEOREM,CUBE ROOTS AND nth ROOTS OF UNITY (INTEGER ANSWER TYPE QUESTION)|1 Videos

  • DIFFERENTIAL EQUATIONS

    IIT JEE PREVIOUS YEAR|Exercise TOPIC 3 APPLICATIONS OF HOMOGENEOUS DIFFERENTIAL EQUATIONS <br> ANALYTICAL & DESCRIPTIVE QUESTIONS|7 Videos

Similar Questions

Explore conceptually related problems

Show that, lim_(n to oo)((1)/(n + 1)+(1)/(n+2)+…+(1)/(6n))=log 6 .

Show that lim_(n rarr oo)((1)/(n+1)+(1)/(n+2)+...+(1)/(6n))=log6

lim_(ntooo) ((n!)^(1//n))/(n) equals

Evaluate lim_(nrarrinfty)((1)/(2n+1)+(1)/(2n+2)+......+(1)/(6n)) .

lim_(ntooo)(n-sqrt(n^(2)+n))

lim_(n rarr oo)[(1)/(n)+(1)/(n+1)+(1)/(n+2)+.....+(1)/(2n)]

lim_(nto oo) {(1)/(n+1)+(1)/(n+2)+(1)/(n+3)+...+(1)/(n+n)} is, equal to

Let f(x)=lim_(ntooo) (x)/(x^(2n)+1). Then