Lim x -1-2-3- n-n-n2-

The correct option is D 1/2We have, lim_x→∞1+2+3+....n/n^2 We know, ∑ n=n(n+1)/2 The limit becomes lim_x→∞n(n+1)/2/n^2 lim_x→∞n(n+1)/2/n^2 = lim_x→∞(n+1)/2n ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Standard Limits to Remove Indeterminate Form

lim x →∞1+2+3...

Question

$lim x \to \infty \frac{1 + 2 + 3 + . . . . n}{n^{2}} =$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\frac{1}{2}$
We have, $lim x \to \infty \frac{1 + 2 + 3 + . . . . n}{n^{2}}$
We know, $\sum n = \frac{n (n + 1)}{2}$
The limit becomes $lim x \to \infty \frac{\frac{n (n + 1)}{2}}{n^{2}}$

$lim x \to \infty \frac{\frac{n (n + 1)}{2}}{n^{2}} = lim x \to \infty \frac{(n + 1)}{2 n}$

$= lim x \to \infty (\frac{1}{2} + \frac{1}{2 n}) = \frac{1}{2} + lim x \to \infty (\frac{1}{2 n}) = \frac{1}{2}$

Suggest Corrections

Similar questions

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

Write the value of ${lim}_{x \to \infty} \frac{1 + 2 + 3 + \dots + n}{n^{2}}$

{lim}_{n \to \infty} \frac{n}{n^{2} + 1} + \frac{n}{n^{2} + 2} + \frac{n}{n^{2} + 3} + . . . . + \frac{n}{n^{2} + n}

Q. Evaluate

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

Q. Evaluate

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

Join BYJU'S Learning Program

limx→∞1+2+3+....nn2=

The correct option is D 12We have, limx→∞1+2+3+....nn2 We know, ∑n=n(n+1)2 The limit becomes limx→∞n(n+1)2n2 limx→∞n(n+1)2n2=limx→∞(n+1)2n =limx→∞(12+12n)=12+limx→∞(12n)=12

$lim x \to \infty \frac{1 + 2 + 3 + . . . . n}{n^{2}} =$