I'm confused how :∞∑n=00=0 but after evaluation we w'd get 0.∞ which it's indeterminate case and wolfram alpha show here that is a convergent series which it's equal's 0, i'm only sure that is 0 for it partial sum .
My question here is : Is there somone who show me how do I convince my self by :∞∑n=00=0 ?
Thank you for any help
Answer
By definition, one has
∞∑n=0an=limN→∞N∑n=0an
giving
∞∑n=00=limN→∞N∑n=00=limN→∞0=0.
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