Induction question (1 Viewer)

[UnrealAnchovies]

Alright, so I saw the induction information already posted and it helped me in some aspects, however I am still struggling with the addition versions. Strangely enough, I find the division and whatnot types far easier than addition, maybe it has something to do with the fact I learned this whilst in year 11? Anyways, I was just looking through some questions and came across this:

1 + 4 + 4^2 + ... + 4^n = 1/3(4^n+1 - 1), for n = 0,1,2,...

Note: 4^n+1 is '4 to the n +1'

Any answer would be much appreciated.
Thanks in advance.

 

[AAEldar]

I proved it true for n=0, but not for n=1 or n=2...So I went with 0. If this is wrong, can someone please correct me haha.

I GIVE UP IT'S NOT WORKING!

Sorry >.> I got it to come out as:

(4^(k+2)-1)/3

If that helps.

 

[UnrealAnchovies]

Hey AAeldar, thanks for the attempt, I think induction is something I definitely need to practice for next year.

 

[AAEldar]

Let's see if this works.

FINALLY! Haha, hopefully that helps you

 

[Flying_Penis]

Easssssssssssssssyyyyyyyyyyyyy

 

[UnrealAnchovies]

THANK YOU AAELDAR!
And yes "Flying Penis" I agree that it's easy for those who haven't self taught the concept of induction...

 

[AAEldar]

THANK YOU AAELDAR!
And yes "Flying Penis" I agree that it's easy for those who haven't self taught the concept of induction...

No worries. Yea, it is hard if you self teach it, some kids in my class even struggled with the help of the teacher. Once you get it though, it's easy.

 

[Pwnage101]

Let's see if this works.

FINALLY! Haha, hopefully that helps you

One (crucial) line is incorrect. should be .