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ashna Group TitleBest ResponseYou've already chosen the best response.0
@waterineyes
 one year ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.0
What are our tool? Are you trying to do this with induction? or do we have modular arithmetic at our disposal?
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
My favourite would be to write it as n(n+1)(n+2) + 3n(n+1) The second term is divisible by 3 and the first one is the product of 3 consecutive integers therefore also divisible by 3. The sum of 2 numbers both divisible by 3 is also divisible by 3.
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
@beginnersmind i didn't get it :/ sorry can u explain it step by step ?
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
According to induction: Put n = 1 and see are you getting what the question says..
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
@beginnersmind do not stop. Carry on.. I am just trying as @ashna is doing..
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
i know that water tell me from , to prove p(k+1) is true
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
My answer didn't use induction so I'd rather not go into a long explanation.
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Ha ha ha ha... You knew that?? Just kidding..
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
we get k = 3M/ (K+1)(K+5) Right ?
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Replace n by k+1 first...
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
yeah did , then ?
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Then Look carefully it will also be divisible by 3.. Ha ha ha ha...
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
c'mon Water i don't understand :I
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
\[= (k+1)(k+2) (k+6)\]
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Really??
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
where r yu goin to substitute k = 3M/ (K+1)(K+5) ?
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Wait...
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
It is now 6 when I studied Induction..
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
*6 years..
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
Ok, this is how you do it with induction. First prove it for n =1 (plug it in and check if it's divisible by 3) Second assume that it's true for P(k). Using this try to prove it's also true for P(k+1) In this case I would try to prove that P(k+1)  P(k) is divisible by 3.
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
yeah .. on assuming i got k = 3M/ (K+1)(K+5) 3rd step am stuck :I
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
what does the M stand for?
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
Ah, ok, see what you did there. You said there's a number M such that P(k) = 3M
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
M = divisible by 3
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
Ok, I'd do it slightly differently. I'd prove that the difference of P(k+1) and P(k) is divisible by 3. Then using this and the induction hypothesis it follows that P(k+1) is also divisible by 3. Does that make sense?
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
Cool :) To check, what did you get for P(k+1)  P(k) ?
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
What if we find the value of k+1 from the assumption??
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
\[k+1 = \frac{3M}{k (k+5)}\]
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
dw:1355641516686:dw
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Hey I don't know how to prove that, I am just giving my Ideas which can be useless too..
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Now this does not look like if it is divisible by 3 or not??
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Wait, do not trust me.. Please confirm it from good source, may be I am wrong because I am not sure..
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
@beginnersmind suggest :)
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
I don't think we are going in the right direction :( Let's just start by checking if the statement holds for n = 1
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
And by let us, I mean you ;)
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
@UnkleRhaukus help here please..
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
Let me rephrase: What's the value of P(1)?
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
divisible by 3 , so true !
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
Ok. So we've proven that it holds for n =1. Now, what's P(k)? P(k+1)?
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
p(k) = 3M / (k+1)(k+5)
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
Let's forget about the induction hypothesis, just express P(k) and P(k+1) using the original definition
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
She has assumed that p(k) is divisible by 3 so 3M where M is an Integer..
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
i dont know how to do other than that :I @beginnersmind
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
I mean, the same way you plugged in n = 1 to get P(1) you can plug in k to get P(k)
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Just replace n by k there..
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
okay so k(k+1)(k=5) = divisible by 3 yu meant this ?
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
p(k) = .......................
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
I mean P(k) = k(k+1)(k+5) We'll use the fact that it's divisible by 3 later, but not yet.
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
okay , now how to proceed ?
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
So the same way, what is P(k+1)?
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
P(k+1) = (k+1)(k+2)(k+6)
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
right
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
We want to look at P(k+1)  P(k)
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
This is the difference between two consecutive terms. For example the difference between the second term and the first term is P(2)P(1)
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
If P(2)  P(1) is divisible by 3 and P(1) is divisible by 3 then so is P(2). Do you see why?
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
Let's try to write out P(k+1)  P(k) and see if it's divisible by 3
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
You already calculated P(k+1) and P(k) separately so just take the difference and see if you can write it in some nice way.
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
It p(1) = 6 p(2) = 8 Then : p(2)  p(1) = 2
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
okay i've got (k+1)[(3k+12)]
 one year ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
This is divisible by 3 now...
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
That's nice. I'd rewrite it as 3(k+1)(k+4) just to emphasize that it's divisible by 3.
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
right YAY :D ty @beginnersmind and @waterineyes
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
Not finished yet. But almost :)
 one year ago

ashna Group TitleBest ResponseYou've already chosen the best response.0
i can do the rest ty :)
 one year ago

beginnersmind Group TitleBest ResponseYou've already chosen the best response.3
Ok :)
 one year ago
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