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

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

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

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

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Calculus

ISBN: 9781285057095

10th Edition

Authors: Ron Larson, Bruce H. Edwards

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Posted Date: Feb 24, 2023 03:18 AM

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

Question:

lim n→∞ 1+2+3+...+n n² HIN 2 lim n→∞ 1+2+3+...+n n² HIN 2

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Calculus

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