God help with Calculus

[Selkie]

So next week is my last week. I have one more test, then a comprehensive final. I'm more worried about the test because one of the main topics that will be included is area under a curve bullshit with the sigma notation shit.

If someone could maybe just flesh out this sample problem and just explain to me what is going on with this garbage, I would be truly grateful:

Find the limit of s(n) as n approaches infinity. s(n) = (18/n^2) [(n(n+1))/2]

[Totla]

go look at bluaki's post

i win

s(n) = (18/n^2) [(n(n+1))/2]
if you multiply that out you would get

[(18)(n^2+n))] / [(n^2)(2)]

(18)(n^2+n)
(n^2)(2)

i guess the second way looks a little nicer. that's a fraction just work with me

so because we're dealing with infinity which is bretty big, things like multiplying by constants doesn't matter, so we can get rid of those

(n^2+n)
(n^2)

also because we're dealing with infinity, n^2 is going to be so much larger than n that it's negligible. think about 10000000^2 compared to 10000000. That discrepancy only gets greater as you approach infinity.

now we're left with

(n^2)/(n^2)

and as we all know anything over itself is 1

someone correct me if i'm wrong i haven't done calc in a while

[bluaki]

so because we're dealing with infinity which is bretty big, things like multiplying by constants doesn't matter, so we can get rid of those

also because we're dealing with infinity, n^2 is going to be so much larger than n that it's negligible. think about 10000000^2 compared to 10000000. That discrepancy only gets greater as you approach infinity.

That first statement is wrong and you would've had the right answer (9) if you didn't throw away the constants. You're probably confusing multiplying by a constant with adding a constant.

The second statement, although correct, wouldn't pass for most tests or proofs

L'Hopital's Rule states that, when evaluating a limit of a fraction for which both numerator and denominator approach infinity (or both zero), the limit of numerator/denominator is equal to the limit of d(numerator)/d(denominator)

given:
18(n^2+n) /
2(n^2)

differentiate both parts:
18(2n+1) /
2(2n)

differentiate both parts again:
18(2) /
2(2)

simplify:
(18 * 2) / (2 * 2) = 9

[silvertone]

looks like bluaki is god


i sorta knew it this whole time.

[Totla]

That first statement is wrong and you would've had the right answer (9) if you didn't throw away the constants. You're probably confusing multiplying by a constant with adding a constant.

The second statement, although correct, wouldn't pass for most tests or proofs

L'Hopital's Rule states that, when evaluating a limit of a fraction for which both numerator and denominator approach infinity (or both zero), the limit of numerator/denominator is equal to the limit of d(numerator)/d(denominator)

given:
18(n^2+n) /
2(n^2)

differentiate both parts:
18(2n+1) /
2(2n)

differentiate both parts again:
18(2) /
2(2)

simplify:
(18 * 2) / (2 * 2) = 9

whoops, my b. i haven't done calc in like half a year
bluaki is correct

[C.Mongler]

u dont know calculus? what a dum dum

[The Hand That Fisted Everyone]

the fuck did i click this thread for