limn→∞∑n(n+3r)3/2,r=0lim_{n\to \infty}\sum \frac{\sqrt{n}}{(n+3r)^{3/2}} , r=0limn→∞∑(n+3r)3/2n,r=0
limn→∞∑n(n)3/2=limn→∞∑1nlim_{n\to \infty}\sum \frac{\sqrt{n}}{(n)^{3/2}}=lim_{n\to \infty}\sum \frac{1}{n}limn→∞∑(n)3/2n=limn→∞∑n1
(Maclaurin–Cauchy test)
limn→∞∑1n∼∫1∞1x=ln(x)∣1∞=∞lim_{n\to \infty}\sum \frac{1}{n} \thicksim \int_{1} ^\infty \frac{1}{x} =ln(x)|_1^\infty=\inftylimn→∞∑n1∼∫1∞x1=ln(x)∣1∞=∞
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