Show that for all large positive integers n the sum 1/(n+1) + 1/(n+2) + 1/(n+3) +...
Show that for all large positive integers n the sum 1/(n+1) + 1/(n+2) + 1/(n+3) + ... + 1/(2n) is approximately equal to 0.693.
I am trying to solve this problem by setting the sigma summation from k = n + k to 2n of 1/j to try to make a harmonic sum but is not working. I let j be n + k so it matches the harmonic sum definition of 1/k
Homework Answers
`Hey,
Note: Brother in case of any queries, just comment in box I would be very happy to assist all your queries
We can rewrite the equation as
Also we know that
Sum of harmonic series with n terms is
Hn=ln(n)+0.5772156649-----eq1
So,
H2n=ln(2n)+0.5772156649-------eq2
Subtract eq1 and eq2
H2n-Hn=ln(2)~0.6931
Kindly revert for any queries
Thanks.
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