Maths Woes... Come forth and prove your brainy-ness

2006-11-05 11:41:54

#1

=Karma-Kills=: "Don't post while intoxicated."; +356|6595|England

Doing my A level maths homework on sequences and series and am getting super stuck on this one questions.

Any help / advice would be much appreciated, and anyone who provides a solution gets a cookie and karma!

Ok,

"Prove that the sum of the first 2n multiples of 4 is 4n(2n+1)"

The formula you need to use is Sn = n/2 (2a + (n-1) d)

Where a is the first term, d is the difference and n is the nth term.

Heres an example at one of my attempts to give you the jist of it...

(n x 4) 4 + 8 + 12 + 16 +....
(2n x 4) 8 + 16 + 24 + 32 +...
a = 8, d = 8, n = 8n

Sn = n/2 (2a + (n-1) d)
S8n = 4n (16 + 64n - 8 )
S8n = 4n (64n + 8)
S8n = 4n (8n + 1)

But we need to get 4n(2n+1),

Thanks for the help!

2006-11-05 11:46:24

#2

samfink: Member; +31|6566

I wish I could help, I'ms tudying A level maths, but ther AS level which doesn't have that. bets thing to do is ask your techer for help,I'm afraid.

2006-11-05 11:49:13

#3

munchagepeople: Member; +3|6647|Bristol, UK

All you need to do is use the formula you posted:

Sn = n/2 * (2a + (n-1) d)

from your question, n = 2n, a = 4, d = 4

plugging these in gives:
(2n/2) * [8 + (2n -1)*4]

canceling and expanding:
= n(8 + 8n - 4)
= 8n + 8n² - 4n
= 8n² + 4n

taking 4n out as a factor:
= 4n(2n +1) as required

2006-11-05 11:50:54

#4

FriiginChomper: Member; +41|6712

shit i hate algebra, i had to do that last year. i went to summer school for that 34% i obtained.
but um.. im guessing "Sn = n/2 (2a + (n-1) d)" is the problem, what number are you solving for and what was the information they gave you, before you solved some of it. its kinda confuzing ><

2006-11-05 11:56:22

#5

=Karma-Kills=: "Don't post while intoxicated."; +356|6595|England

munchagepeople wrote:
All you need to do is use the formula you posted:

Sn = n/2 * (2a + (n-1) d)

from your question, n = 2n, a = 4, d = 4

plugging these in gives:
(2n/2) * [8 + (2n -1)*4]

canceling and expanding:
= n(8 + 8n - 4)
= 8n + 8n² - 4n
= 8n² + 4n

taking 4n out as a factor:
= 4n(2n +1) as required

You make it seem oh soo simple!

Thanks so much man, that was starting to do my head in... just forgot to take out factors...

As promised

https://wiki.coolmon.org/files/cookie.jpg

+1 to you my man!

https://www.galleryone.com/images/bullas/bullas-ps-i-love-you.jpg

2006-11-05 11:57:09

#6

teehee1988: Member; +5|6649|Birmingham, UK

Yeah or do
a=4
d=4
n=n
the multiply all by 2 at the end
all fun and frollics with A2 maths

2006-11-05 11:58:09

#7

liquidat0r: wtf.; +2,223|6638|UK

Its amazing how, when something is explained in a different way; it immediately becomes simple.

2006-11-05 12:00:13

#8

..teddy..jimmy: Member; +1,393|6660

[fail at math]..teddy..jimmy[/cant do math for shit]

2006-11-05 12:00:16

#9

=Karma-Kills=: "Don't post while intoxicated."; +356|6595|England

liquidat0r wrote:
Its amazing how, when something is explained in a different way; it immediately becomes simple.

I know exactly what you mean. It annoys me so much how teachers make it look so simple, just by looking at the problem in a different way, or taking that one extra step.

Anyways, christmas must have come early becuase,

KARMA FOR ALL

2006-11-05 12:02:33

#10

munchagepeople: Member; +3|6647|Bristol, UK

teehee1988 wrote:
Yeah or do
a=4
d=4
n=n
the multiply all by 2 at the end
all fun and frollics with A2 maths

or you can always use the generic sum of series formula:

sum of i from i=1 to n = n(n+1) / 2

you have the sum of 4i from i = 1 to 2n, so:

= 4 * [2n(2n + 1) / 2]

which comes out as the same answer

2006-11-05 12:07:36

#11

=Karma-Kills=: "Don't post while intoxicated."; +356|6595|England

The quality and quantity and of the responses has restored my faith in these forums... and yes... even humanity itself.

yay

https://img501.imageshack.us/img501/6503/carltonda8.gif

Last edited by =Karma-Kills= (2006-11-05 12:08:00)

2006-11-05 12:20:09

#12

FrankieSpankie3388: Hockey Nut; +243|6541|Boston, MA

Wait until you reach Calculus. I'm in Honors calc, here's an example of one problem from my homework:

Find the derivitive of cos(1-2x)^2 and that's the EASY question! Luckily we only got review for homework and it's all easy, but some of this other stuff is hard as hell, like find the derivitive of 3cos^3(2x-2)^4-2sin(4x^2+2x-5)^2

2006-11-05 12:21:37

#13

=Karma-Kills=: "Don't post while intoxicated."; +356|6595|England

FrankieSpankie3388 wrote:
Wait until you reach Calculus. I'm in Honors calc, here's an example of one problem from my homework:

Find the derivitive of cos(1-2x)^2 and that's the EASY question! Luckily we only got review for homework and it's all easy, but some of this other stuff is hard as hell, like find the derivitive of 3cos^3(2x-2)^4-2sin(4x^2+2x-5)^2

Summin to look forward to!

PS by the derivative, do you mean differentiate (eg. dy/dx)?

2006-11-05 12:43:36

#14

FrankieSpankie3388: Hockey Nut; +243|6541|Boston, MA

Yup, sucks because there's like 18 steps when it comes down to those huge problems and it's so easy to fuck up.

2006-11-05 13:06:20

#15

-TL-: Srs lurker; +25|6504|Oklahoma City

Yeah, simply taking the derivative can be the worst part of calculus, since the teacher often gives you a real doozy for a function just to make sure you know your stuff.

2006-11-05 13:08:53

#16

Naughty_Om: Im Ron Burgundy?; +355|6644|USA

=Square root of your mom

2006-11-05 13:08:56

#17

Naughty_Om: Im Ron Burgundy?; +355|6644|USA

=Square root of your mom

2006-11-05 13:12:55

#18

Jbrar: rawr; +86|6553|Winterpeg, Canada

I did this stuff last month in class, whoever is teaching you that shit is telling you to do extra steps which just end up confusling you.

2006-11-05 13:25:32

#19

munchagepeople: Member; +3|6647|Bristol, UK

FrankieSpankie3388 wrote:
Wait until you reach Calculus. I'm in Honors calc, here's an example of one problem from my homework:

Find the derivitive of cos(1-2x)^2 and that's the EASY question! Luckily we only got review for homework and it's all easy, but some of this other stuff is hard as hell, like find the derivitive of 3cos^3(2x-2)^4-2sin(4x^2+2x-5)^2

bah, that kind of calculus is easy - it's just taking the simple rules (chain, product, quotient etc.) and applying them all as many times as necessary to get the result you want.

See this thread for some more interesting calculus-y kinds of question - the two I solved might be a little advanced for most of you though

BF2S Forums Maths Woes... Come forth and prove your brainy-ness

munchagepeople wrote:

liquidat0r wrote:

teehee1988 wrote:

FrankieSpankie3388 wrote:

FrankieSpankie3388 wrote:

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