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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

Solve using Sandwich Theorem-


lim (n tends to infinity) 1 + 1/2^2+ 1/3^2+ 1/4^2 +....+1/n^2

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
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 & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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