The Student Room Group

Prove by induction

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Where did I mess up?
Original post by ckfeister
question5.PNG
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Where did I mess up?


By putting the -1 in the square brackets.

Move it off to the end of the line before you start, and hopefully things will be clearer.
yes need to leave the -1 to one side & factorise the other bits.
Reply 3
Original post by ghostwalker
By putting the -1 in the square brackets.

Move it off to the end of the line before you start, and hopefully things will be clearer.


Original post by the bear
yes need to leave the -1 to one side & factorise the other bits.


This still does not make any sense to me... maybe illustrate it?
Reply 4
Original post by ghostwalker
By putting the -1 in the square brackets.

Move it off to the end of the line before you start, and hopefully things will be clearer.


Original post by the bear
yes need to leave the -1 to one side & factorise the other bits.


Oh I get the part about -1 ...but I get this....
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Original post by ckfeister
Oh I get the part about -1 ...but I get this....


(k+1)!(k+2)=(k+2)!(k+1)!(k+2)=(k+2)!
Reply 6
Original post by RDKGames
(k+1)!(k+2)=(k+2)!(k+1)!(k+2)=(k+2)!


Didn't know about this, whats the general rule for this stuff?/theory name (if you know)... thx
(edited 6 years ago)
Original post by ckfeister
Didn't know about this, whats the general rule for this stuff?


Really?

n!(n+1)=(n+1)!n!(n+1)=(n+1)! which should be a pretty common result to know if you know about factorials.

n!=12...nn!=1\cdot 2\cdot ... \cdot n so n!(n+1)=(12...n)(n+1)=(n+1)!n!(n+1)=(1\cdot 2\cdot ... \cdot n )\cdot (n+1)=(n+1)! by definition.
(edited 6 years ago)
Reply 8
Original post by RDKGames
Really?

n!(n+1)=(n+1)!n!(n+1)=(n+1)! which should be a pretty common result to know if you know about factorials.

n!=12...nn!=1\cdot 2\cdot ... \cdot n so n!(n+1)=(12...n)(n+1)=(n+1)!n!(n+1)=(1\cdot 2\cdot ... \cdot n )\cdot (n+1)=(n+1)! by definition.


Oh the extra term thing... my logic isn't good you see... its improving though... hopefully.
Original post by ckfeister
Didn't know about this, whats the general rule for this stuff?/theory name (if you know)... thx


factorials is just the product of the numbers from 1 up to where you are.

so if you have ( k + 1 )! then times by the next number above, you get ( k + 2 ) !

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