Problem: test if the series converges∞∑n=1(−2)n+1nn+1
My approach:
I see it is equal to ∞∑n=1(−2)nnn⋅−2n, and ∑∞n=1(−2)nnn converges absolutely using root test, and ∑∞n=1−2n diverges by using p-series test.
So is the original series divergent because convergent * divergent = divergent?
Is convergent * convergent = convergent??
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