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Prove these questions by using the definition of convergence of a sequence. lim n 1+2+3+...+n n HIN 2

Prove these questions by using the definition of convergence of a sequence.

$( lim _{n ightarrow infty} frac{1+2+3+ldots+n}{n^{2}}=frac{1}{2} )$

$( lim _{n ightarrow infty}(sqrt{n+1}-sqrt{n})=0 )$

lim n 1+2+3+...+n n HIN 2

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