Grade 12Differential Calculus

Solve using Sandwich Theorem-

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

Pallabi Mishra

16 Years agoGrade 12

1 Answer

Jitender Singh

11 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

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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

Pallabi Mishra

1 Answer

Jitender Singh

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