Find an expression, in terms of n, for the coefficient of x in the expansion of
(1+4x)+(1+4x)^2+(1+4x)^3+...+(1+4x)^n

Question

Find an expression, in terms of n, for the coefficient of x in the expansion of 
(1+4x)+(1+4x)^2+(1+4x)^3+...+(1+4x)^n

shubhamsrg · Answer

its an GP if you observe properly,,which solves 90% of the question..

anonymous · Answer

a wat

shubhamsrg · Answer

geometric progression.. o.O

anonymous · Answer

yup, got that.

anonymous · Answer

so, what do i do with that??

shubhamsrg · Answer

sum of n terms of geometric progression ?

anonymous · Answer

oh wait. 

n/2 (a + l)

anonymous · Answer

ok, but i don't need to find the sum. i know a and l.

shubhamsrg · Answer

nah you dont have a clue! :/

anonymous · Answer

awww, come on. help me.

anonymous · Answer

I have this thing due tomorrow, and i REALLY need help.

shubhamsrg · Answer

too bad,,unless you try yourself, i cant help..

you should study about GPs firstly..

anonymous · Answer

I have :P

anonymous · Answer

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

shubhamsrg · Answer

what is the sum formulla for AP then ?

anonymous · Answer

Wait, that's what I wrote above. Then i don't know GP. but i googled it and found stuff on wikipedia.

anonymous · Answer

that we multiply th whole thing with the common ratio,and then subtract it, so we get the sum. But even then, how would the sum help us??

shubhamsrg · Answer

after you get the sum you can use binominal expansion..

anonymous · Answer

i'm sorry, i don't understand:P Use binomial expansion how??

shubhamsrg · Answer

nevermind,,study harder..one day you shall be able to do the question yourself :P

anonymous · Answer

listen, PLEASE PLEASE PLEASE help me. I'm desperate.

anonymous · Answer

being this 'enigmatic' is REALLY infuriating. just, please.

anonymous · Answer

My teacher will KILL me.

anonymous · Answer

Please. PLEASE. I need help, obviously.

shubhamsrg · Answer

am sure someone else would help you here//not me,,am the wrong person! ;)

anonymous · Answer

are you kidding?? you say all this stuff, and then just say 'i'm not gonna help you"?? wow, yeahh, real helpful you've been.

shubhamsrg · Answer

you dont know GP and you probably also dont know binomial expansion, you dont deserve the direct solution i'd say! :D

you got to work for it,,its no freebie..
and yes indeed i've been real helpful! ;)

anonymous · Answer

ummm, yeahh, i actually DO know binomial. I would have done that a LONG time ago, if it wasn't for the 'in term of n' thing.

anonymous · Answer

and if i had to 'work' for it, i wouldn't have needed help.

shubhamsrg · Answer

lol..i find your argument really amusing! :D

anonymous · Answer

4x + 8x+ 12x +...+ 4nx
taking 4x common
4x (1+2+3+...+n)
4x [n(n+1)/2]
2x[n(n+1)]

so 2n(n+1) is the co efficient

anonymous · Answer

but you can't just TAKE 4x common, that stuff has powers.

shubhamsrg · Answer

i see what you did @rizwan_uet !! nice..excellent solution..
you should try and figure out what he did @tanvidais13 in the mean time! :P

anonymous · Answer

yes but that are high power of x so i just mentiones the the terms with x only

anonymous · Answer

i m warned by moderator lol

shubhamsrg · Answer

hmmm..

anonymous · Answer

@tanvidais13 you got my point

shubhamsrg · Answer

i bet my ipod for this she didnt! :P

anonymous · Answer

hahahah

anonymous · Answer

i get it, you took the powers down, blah blah blah.

anonymous · Answer

exaclty

shubhamsrg · Answer

powers down hmm? how come.. ?

shubhamsrg · Answer

blah blah blah tells rest of the story! :D

raden · Answer

it can be :
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