Mathematical Induction - Guessing? (1 Viewer)

[243_robbo]

We have jsut covered 4 Unit induction and i am a bit thrown off by the concept of "Guessing" the formula to use as a method in some of the question. Is there any logical way to do this or is it just trial and error?

 

[Raginsheep]

What do you mean by guessing? Anyone examples?

 

[243_robbo]

for example:

Q15 Ex 37(c) - JB Fitzpatrick

Guess a formula for Un, and then attempt to prove by induction that the guess is correct for all natural numbers n.

Un = 1 x 2 +2 x 3 + 3 x 4 + … + n (n + 1)



Answer is:

n(n + 1)(n + 2)
3 <--- all over

 

[243_robbo]

i got the answer from the book but i cannot see the logical way to get to it other than T&E

 

[Riviet]

Try letting n=1, 2, and 3 and substitute each value of n into your series or expression U_n and write an unsimplified expression, ie e.g for n=1, keep it as 1 x 2 instead of simplifying it. Then compare and contrast each expression and try to hypothesis the formula.

 

[243_robbo]

its the hypothesis bit that bugs me. like i was trying to find some expression for - 1,4,9,16, etc and it took me like ten minutes to realise it was just sqares..

 

[Raginsheep]

Its guessing but only to the exent of seeing a pattern. Then it becomes just using induction to prove that your pattern is correct.

I wouldn't worry too much about it though, I've rarely seen such questions and of those I have seen, the formula is pretty easy to see.

 

[243_robbo]

koolies