2.1.47 Calculation of Limits
Condition: calculate the limits: a) \ (\ lim _ {n \ rightarrow \ infty} \ left (\ frac {\ sqrt {1+2+3+\ cdots+n}}} {2 n+1} -2 n \ right) \), b) \ (\ lim _ {n \ rightarrow \ infty} \ left (\ frac {\ sqrt {n^{2} +1} +2} {\ sqrt {n^{2} +1} +4} \ right)^{2 n} \).
Calculation of Various Limits, Using L'Hopital's Rule, Remarkable Limits, Power Series, Equivalent Values of Various Other Methods.