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        Solve using Sandwich Theorem-
lim (n tends to infinity) 1 + 1/2^2+ 1/3^2+ 1/4^2 +....+1/n^2
7 years ago

Jitender Singh
IIT Delhi
158 Points
										Ans:$L = \lim_{n\rightarrow \infty }\sum_{r=1}^{n}(\frac{1}{r^{2}})$$\frac{1}{r^{3}}<\frac{1}{r^{2}}<1$$\sum \frac{1}{r^{3}}<\sum \frac{1}{r^{2}}<\sum 1$$\lim_{n\rightarrow \infty }\sum_{r=1}^{n}1 = \infty$$\lim_{n\rightarrow \infty }\sum_{r=1}^{n}(\frac{1}{r^{3}})$→This is a divergent series, so it will also tend to infinity.Acording to sandwich theorm, L will also approaches to infinity.Thanks & RegardsJitender SinghIIT DelhiaskIITians Faculty

3 years ago
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