binomial theorem (2 Viewers)

[dawso]

here are 2 questions out of geha's excel step by step guide 2 3unit, i am 90% sure i got both right but he is wrong, wat do u guys get 4 em??

example 2 - find the coefficient of x^2 in the expansion of:

(x^2 + 3/x) ^10

review question 2 - find the term independent of x in the expansion of:

(2x - 1/4x^3) ^20

thanks in advance all

-dawso

ps- dont buy this book, the number of typos in it is so bad, i cant be fuked doin any more questions out of it cause the solutions are wrong

 

[Templar]

(2x - 1/4x^3) ^20

Is that (2x-(1/4)x^3)^20?

 

[Slidey]

Wouldn't it be (2x-1/(4x^3))^20? Otherwise when it asks for 'independant term', that would be meaningless. I presume independant term is another way of saying constant.

 

[acmilan]

I presume independant term is another way of saying constant.

Thats right

 

[withoutaface]

(x^2 + 3/x) ^10

By inspection it is 3⁶10C6

(2x - 1/4x^3) ^20

By inspection it is -2¹⁵ 20C5/4⁵=-2⁵ 20C5

 

[dawso]

thank u withoutaface, u hav confirmed my belief that geha is wrong! i got the same as you..... out of interest but, how do u just go 'by inspection,' ...are u sayin u can do that in ur head??

 

[DeeBee]

im not sure where the brackets are supposed to be in the second question.
but for the first one i got 153090x^2.
does that sound right? or am i way off?
i used the general term rule thingy

 

[DeeBee]

induction

has anyone touched on induction?
i missed my last class cos i thought i had a free...moron i know..
anyway so now im kinda lost..like...how would you solve this? step by step...and stick in the obvious too please...
use mathematical induction to show that 3^n + 7^n is divisible by 10 for all odd positive integers n>=1
help!

 

[Templar]

but for the first one i got 153090x^2.

You're right. I'm getting way too lazy recently, plugging everything into Mathematica and getting an answer instead of working it out by hand.

 

[DeeBee]

that was a joke right?

 

[withoutaface]

thank u withoutaface, u hav confirmed my belief that geha is wrong! i got the same as you..... out of interest but, how do u just go 'by inspection,' ...are u sayin u can do that in ur head??

By inspection means instead of using algebra I just play around with numbers in my head until I get the independent term or whatever the question asks.

 

[dawso]

yeah i thought so m8, so as i said, u did this in ya head, dayem.....

anyway, the important thing that we hav established here is that i am smarter than geha, game, set and match!!