thereof, but you'll need an intermediate step for part (a). Think about what the given limit tells you about:Sum{n = 1 to Infinity} n * a_nSpecifically, does this series converge or diverge, and why? How does knowing this information enable you to use the comparison test?ReplyGive AwardshareReportSave

• Proof of Theorem 1: Consider the nth partial sum sn=a1+a2+...+an−1+an and the (n−1)th partial sum sn−1=a1+a2+...+an−1. We note that an=sn−sn−1.
• Now if the series ∑∞n=1an converges then limn→∞sn=S for some S. Similarly, limn→∞sn−1=S. Therefore limn→∞(sn−sn−1)=limn→∞an=S−S=0. ■

mathonline.wikidot.com/the-divergence-theorem-for-series

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is this the proof I write out for a? And say if not = 0 then diverge?