∑(n:0->∞) (n+1)/(2n+1)
(n+1)/(2n+2) < (n+1)/(2n+1)
1/2 < (n+1)/(2n+1) (1)
(n+1)/(2n+1) < (2n+1)/(2n+1) =1 (2)
1/2 < (n+1)/(2n+1) < 1
lim(n->∞) n/2 < ∑(n:0->∞) (n+1)/(2n+1) < lim(n->∞) n
=>
∑(n:0->∞) (n+1)/(2n+1) -> ∞
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