- #1
mynameisfunk
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could someone please help me I am urgent & desperate
True or False, give proof or counterexample
(1) If [itex]a_n \geq 0[/itex] for all [itex]n[/itex] and [itex]\sum a_n[/itex] converges then [itex]na_n \rightarrow 0[/itex] as [itex]n \rightarrow \infty[/itex].
(2) if [itex]a_n \geq 0[/itex] for all n and [itex]\sum a_n[/itex] converges, then [itex]n(a_n-a_{n-1}) \rightarrrow 0[/itex] as [itex]n \rightarrow \infty[/itex].
I thought i had it solved by setting [itex]a_n[/itex] to [itex]1/(n^2)[/itex]
Homework Statement
True or False, give proof or counterexample
(1) If [itex]a_n \geq 0[/itex] for all [itex]n[/itex] and [itex]\sum a_n[/itex] converges then [itex]na_n \rightarrow 0[/itex] as [itex]n \rightarrow \infty[/itex].
(2) if [itex]a_n \geq 0[/itex] for all n and [itex]\sum a_n[/itex] converges, then [itex]n(a_n-a_{n-1}) \rightarrrow 0[/itex] as [itex]n \rightarrow \infty[/itex].
Homework Equations
The Attempt at a Solution
I thought i had it solved by setting [itex]a_n[/itex] to [itex]1/(n^2)[/itex]