Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Compute the sum and the limit of the sum as $n \rightarrow \infty.$$$\sum_{i=1}^{n} \frac{1}{n}\left[\left(\frac{i}{n}\right)^{2}+2\left(\frac{i}{n}\right)\right]$$

$$=\frac{2}{6}+1=\frac{4}{3}$$

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Integration

Section 2

Sums and Sigma Notation

Integrals

Integration Techniques

Campbell University

Oregon State University

Baylor University

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

03:46

Compute the sum and the li…

02:46

04:30

02:00

Evaluate $$\sum_{n=1}^{\in…

02:30

Evaluate $\sum_{n=1}^{\inf…

00:08

Express the limit as a def…

01:15

Find the sum of the series…

02:45

Find the sum of the two in…

01:16

03:13

Show that $$\sum_{n=1}…

I just really want to find the full information. So let's start by Rick News up into two creation. So we have one over N that I over end luxury ice on us. I squared over ends word and we have plus decimation of one over n squared. So what? It's here that this n values a constant so we can just factor that out. Three at one over and you summation from ice equal to one to end of I squared across one over and squared Summation of one from eyes, people to one toe. So now let's use equation in three. And this is equation one. I'm doing a 2.1 said if you have this one over and Cube times are last time, which is on times and plus one sometimes to end plus one over six and then we have plus one over and squared times. I lost him in an entire to constantly Okay, just simplify. Yes. Yet end with one to end close one over and squared times and plus one over end. Okay, so this is our station. And now we want to find the limits as and approaches. Oh, Was it approaches Infinity clothes, a multiply out earning writer here. So we have to and squared plus green on an influx one over until about two. Time six and n plus one over. And so from Mr here we can divide by our our high stone threats equal to the limits as an approaches infinity off two plus three over end, plus one over and squared over six. And then we have plus the limits as on approaches infinity of one over at I would actually fruit this time right here. Let's combine this into distraction So we multiply this term by Yeah, let's get out first before we actually divide by our house Far who will have to you any squared but three and plus one An inquest will multiply this by six on on both sides. So we get six n over 600 Skway. So this is equity six plus three just x 789 in. Okay, I know we'll divide by our highest powers. That's and quit. We get the limit as an approaches Infinity of two plus nine over end, post one over and squared over six. So taking our limit These cancel these becomes Errol Under left with our limits is equal to 2/6 and that's equal to 1/3

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

Compute the sum and the limit of the sum as $n \rightarrow \infty.$$$\su…

Evaluate $$\sum_{n=1}^{\infty} \frac{1}{n(n+1)(n+2)}$$ (Hint: $\frac{1}{n(n+…

Evaluate $\sum_{n=1}^{\infty} \frac{n}{2^{n}} .$ Hint: Use differentiation t…

Express the limit as a definite integral.$$\lim _{n \rightarrow \infty} …

Find the sum of the series.

$ \sum_{n = 0}^{\infty} (-1)^n \frac {x^…

Find the sum of the two infinite series $\sum_{n=1}^{\infty}\left(\frac{2}{3…

Find the sum of the series $$\sum_{n=2}^{\infty} \ln \left(1-\frac{1}{n^…

Show that $$\sum_{n=1}^{\infty} \frac{n !}{n^{n}}$$converges. Hint: …

04:03

Use mathematical induction to prove that $\sum_{i=1}^{n} i^{3}=\frac{n^{2}(n…

09:45

A function $f$ has a slant asymptote $y=m x+b(m \neq 0)$ if $\lim _{x \right…

00:27

Find the general antiderivative.$$\int\left(4 x-2 e^{x}\right) d x$$

19:19

List the evaluation points corresponding to the midpoint of each sub interva…

03:08

Find all critical numbers by hand. If available, use graphing technology to …

Suppose a chemical reaction follows the equation $-x^{\prime}(t)=c x(t)[K-x(…

00:29

Find the general antiderivative.$$\int \frac{3}{4 x^{2}+4} d x$$

02:09

Compute sums of the form $\sum_{i=1}^{11} f\left(x_{i}\right) \Delta x$ for …

01:54

Show that $\lim _{x \rightarrow 0} \frac{\sin k x^{2}}{x^{2}}$ has the indet…

01:17

Sketch a graph of a function $f$ such that the absolute maximum of $f(x)$ on…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.