Skip to main content
MathOverflow

Return to Answer

added 6 characters in body
Source Link
Iosif Pinelis
Iosif Pinelis
  • 127.7k
  • 8
  • 107
  • 229

The expression under the limit sign in question is just a Riemann sum for $$\int_0^1 \frac12\,\Big(\frac1x-\cot x\Big)\,dx=\frac12\,\ln\frac\pi2,$$$$\int_0^{\pi/2} \frac12\,\Big(\frac1x-\cot x\Big)\,dx=\frac12\,\ln\frac\pi2,$$ which therefore is the value of the limit.

The expression under the limit sign in question is just a Riemann sum for $$\int_0^1 \frac12\,\Big(\frac1x-\cot x\Big)\,dx=\frac12\,\ln\frac\pi2,$$ which therefore is the value of the limit.

The expression under the limit sign in question is just a Riemann sum for $$\int_0^{\pi/2} \frac12\,\Big(\frac1x-\cot x\Big)\,dx=\frac12\,\ln\frac\pi2,$$ which therefore is the value of the limit.

Source Link
Iosif Pinelis
Iosif Pinelis
  • 127.7k
  • 8
  • 107
  • 229

The expression under the limit sign in question is just a Riemann sum for $$\int_0^1 \frac12\,\Big(\frac1x-\cot x\Big)\,dx=\frac12\,\ln\frac\pi2,$$ which therefore is the value of the limit.