navygoat5871
11.10.2019 •
Mathematics
Convergence of riemann zeta function when s=3
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Ответ:
Writing the infinite series as a limit of a partial sum, you can see that the series represents the left-endpoint Riemann approximation to the function :
In particular, since is a concave function for , i.e. strictly decreasing and approaching 0 as , which means the Riemann sum approximation is greater than the value of the integral.
So the value of the series is some real number smaller than 2 (actually somewhere around 1.202).
Long story short: use the integral test for determining whether the series converges.
Ответ:
Do you want a answer or explain.