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the term goes to 1 as n goes to infinity

its basically n/n
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as n gets large, the "+1" matters less and less, and "(n+1)/n" starts looking more and more like "n/n", which is equal to 1. So the limit of 2/5\*((n+1)/n)^2 = 2/5\*1^2 = 2/5.
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If you wanted you could just use L'Hospital's rule. It becomes 1/1 which is 1.
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lim \[ (2/5) ( (n+1)/n )^(2) \]

= (2/5) lim \[ ( (n+1)/n )^(2) \]

= (2/5) \[ lim (n+1)/n \]^(2)
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