help pls
#INDUCTION
fervent ravine
main brambleBOT
help pls
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stuck gazelle
,rccw
signal compassBOT
stuck gazelle
Show that the statement is true for $n=1$, then true for $n=k+1$, with $k\in\bN$. Then conclude using the inductive hypothesis.
signal compassBOT
Kocher
stuck gazelle
this how far ive gotten
You can just use the fact that $6^{k+1}-1=6^{k+1}-6+5$.
signal compassBOT
Kocher
stuck gazelle
So you can use the inductive hypothesis cleverly.
fervent ravine
what im completeyly lost
stuck gazelle
You need to find a way to use the fact that $6^k-1$ is divisible by 5, per your inductive hypothesis.
signal compassBOT
Kocher
stuck gazelle
If you can find a clever way to group the terms such that this hypothesis appears, you'll be virtually done with the proof.
polar tide
You can just use the fact that $6^{k+1}-1=6^{k+1}-6+5$.
Technically, both ways will give the answer, since:
||a^(n + 1) - b^(n + 1) = a(a^n - b^n) + (a - b)b^n = b(a^n - b^n) + (a - b)a^n||
fervent ravine
idk what youse are on abt if u look at my example i sent could you compare to q im doing now and tell me whats the next thing i have to write
stuck gazelle
Technically, both ways will give the answer, since:
||a^(n + 1) - b^(n + 1) = a(...
Yeah, but depending on the context, the formula may not be able to be used.
Anyways.
,rccw
signal compassBOT
signal compassBOT
stuck gazelle
idk what youse are on abt if u look at my example i sent could you compare to q ...
You've done exactly that in your previous examples. You've found a way to use the fact that (something) is divisible by (something).
stuck gazelle
theres more to that
I know.
stuck gazelle
You've done exactly that in your previous examples. You've found a way to use th...
Now you just have to find a way to include (6^k-1) in your statement, which will convienienty have a multiple of 5.
fervent ravine
why positive
fluid spoke
Kocher sorry for interrupting but he has done some mistakes here
Why did you write -1 in the power in the 2nd step
And how did you take out 6² in the last step
stuck gazelle
-36+35=-1.
fervent ravine
Kocher sorry for interrupting but he has done some mistakes here
Why did you wr...
oh ye my bad
taht - 1 isint ment to be apart of the power
and the 6^2 i took out bc thats what i did in my exampkle
fluid spoke
**Kocher**
So do it again and use what kocher said
polar tide
Yeah, but depending on the context, the formula may not be able to be used.
Hm, why? It can be used for the induction step for all of these exercises.
stuck gazelle
Hm, why? It can be used for the induction step for all of these exercises.
Sure, but it's kind of a cheat code.
polar tide
Sure, but it's kind of a cheat code.
Well, I guess. It's easy to derive, though.
fervent ravine
i ahve this q aswell
but im confused
on how to get the -3.4^k + 1
part
@stuck gazelle @fluid spoke @polar tide
fluid spoke
I don't understand what you did in
fervent ravine
?
fluid spoke
polar tide
I'd represent 7 = 3 + 4.
fervent ravine
what does that mean
polar tide
Ah, wait! Sorry, I misread.
polar tide
Ah, I see now.
Yeah, looks good.
polar tide
but idk how i got the -3.4^k - 6
Well, we had 4*4^k + 1, but the bracket term contains 7*4^k + 7. That's 3*4^k + 6 more than what we had, so we subtract it.
fervent ravine
is the bracket not( 7^k + 4^k + 1 )
polar tide
is the bracket not( 7^k + 4^k + 1 )
The first term is 7(7^k + 4^k + 1) = 7*7^k + 7*4^k + 7.
fluid spoke
You can +close if you don't have anymore questions
fervent ravine
+close
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