It is known that +∞∑n=11n is divergent. Also, it is known that +∞∑n=11pn is divergent where pn is n-th prime number.
I was thinking what would happen (in the sense of convergence) if we termwise subtract these two series to obtain +∞∑n=1(1n−1pn)
Is +∞∑n=1(1n−1pn) convergent?
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