Find - limn - 12 - 22 - 32 - 42 - 52 - -n terms-n2

lim_n→ ∞1^2 2^2+3^2 4^2+5^2+...n termsn^2 =lim_n→ ∞(1^2 2^2)+(3^2 4^2)+(5^2 6^2)+...n termsn^2 =lim_n→ ∞(1 2)(1+2)+(3 4)(3+4)+(5 6)(5+6)+...n ter ...

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Definite Integral as Limit of Sum

Find : limn ...

Question

Find :
$lim n \to \infty \frac{(1^{2} - 2^{2} + 3^{2} - 4^{2} + 5^{2} + . . . . . . n t e r m s)}{n^{2}}$

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lim n \to \infty \frac{(1^{2} - 2^{2} + 3^{2} - 4^{2} + 5^{2} + . . . . n t e r m s)}{n^{2}}

lim n \to \infty [\frac{\sqrt{n^{2} - 1^{2}}}{n^{2}} + \frac{\sqrt{n^{2} - 2^{2}}}{n^{2}} + \frac{\sqrt{n^{2} - 3^{2}}}{n^{2}} + \dots . n t e r m s] =

1^{2} - 2^{2} + 3^{2} - 4^{2} + 5^{2} - 6^{2} + \dots n terms

\sqrt{1 + \frac{1}{1^{2}} + \frac{1}{2^{2}}} + \sqrt{1 + \frac{1}{2^{2}} + \frac{1}{3^{2}}} + \sqrt{1 + \frac{1}{3^{2}} + \frac{1}{4^{2}}} + . . . . n terms

lim n \to \infty \frac{(1 + 2 + 3 + \dots \dots + n terms) . (1^{2} + 2^{2} + \dots \dots n terms)}{n (1^{3} + 2^{3} + . . . + n terms)}

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