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induction

@beginnersmind i didn't get it :/ sorry
can u explain it step by step ?

According to induction:
Put n = 1 and see are you getting what the question says..

@beginnersmind do not stop.
Carry on..
I am just trying as @ashna is doing..

i know that water tell me from ,
to prove p(k+1) is true

My answer didn't use induction so I'd rather not go into a long explanation.

Ha ha ha ha...
You knew that??
Just kidding..

we get k = 3M/ (K+1)(K+5) Right ?

Replace n by k+1 first...

yeah did , then ?

Then Look carefully it will also be divisible by 3..
Ha ha ha ha...

c'mon Water i don't understand :I

\[= (k+1)(k+2) (k+6)\]

okay

Really??

where r yu goin to substitute k = 3M/ (K+1)(K+5) ?

Wait...

okay

It is now 6 when I studied Induction..

*6 years..

yeah .. on assuming i got k = 3M/ (K+1)(K+5)
3rd step am stuck :I

what does the M stand for?

Ah, ok, see what you did there. You said there's a number M such that P(k) = 3M

M = divisible by 3

yes :)

Cool :)
To check, what did you get for P(k+1) - P(k) ?

What if we find the value of k+1 from the assumption??

\[k+1 = \frac{3M}{k (k+5)}\]

|dw:1355641516686:dw|

Hey I don't know how to prove that, I am just giving my Ideas which can be useless too..

Now this does not look like if it is divisible by 3 or not??

yeah .. :P

@beginnersmind suggest :)

okay !

And by let us, I mean you ;)

@UnkleRhaukus help here please..

Let me rephrase:
What's the value of P(1)?

12

divisible by 3 , so true !

Ok. So we've proven that it holds for n =1.
Now, what's
P(k)?
P(k+1)?

p(k) = 3M / (k+1)(k+5)

She has assumed that p(k) is divisible by 3 so 3M where M is an Integer..

i dont know how to do other than that :I
@beginnersmind

I mean, the same way you plugged in n = 1 to get P(1) you can plug in k to get P(k)

Just replace n by k there..

okay so k(k+1)(k=5) = divisible by 3
yu meant this ?

p(k) = .......................

I mean P(k) = k(k+1)(k+5)
We'll use the fact that it's divisible by 3 later, but not yet.

okay , now how to proceed ?

So the same way, what is P(k+1)?

P(k+1) = (k+1)(k+2)(k+6)

right

and now ?

We want to look at P(k+1) - P(k)

why ?

okay

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?

yes i do

Let's try to write out P(k+1) - P(k) and see if it's divisible by 3

It p(1) = 6
p(2) = 8
Then : p(2) - p(1) = 2

okay i've got (k+1)[(3k+12)]

This is divisible by 3 now...

That's nice. I'd rewrite it as 3(k+1)(k+4) just to emphasize that it's divisible by 3.

right YAY :D
ty @beginnersmind and @waterineyes

Not finished yet.
But almost :)

i can do the rest ty :)

Ok :)