induction help (1 Viewer)

[oredbayz]

hey,

just encountered an issue with induction when testing the base case n=2 given n>=2



i thought it was only if n=1 we test the first value 1/2^2, but since n>=2, we test n=2 which includes the first 2 terms 1/2^2 + 1/3^2 but this isn't the case with HSC solutions, eddie woo includes the first 2 terms for n>=2 see eddie woo

 

[cossine]

In this case n = 2 does not correspond to the second term. If the base case was n =1 then n=2 will mean you are adding two terms.

 

[oredbayz]

In this case n = 2 does not correspond to the second term. If the base case was n =1 then n=2 will mean you are adding two terms.

since base case is n=2, it should include first and second term as eddie woo explains in the video

 

[cossine]

since base case is n=2, it should include first and second term as eddie woo explains in the video

I think it comes down to the interpretation of the problem. Perhaps in Eddie Woo case that was appropiate, but in this problem it is presumably not.

You can see there is no "1/1^2" term on the LHS.

 

[stupid_girl]

The proposition is not defined for n=1. You are the required to prove the proposition for n>=2 and the base case is n=2, which has only 1 term.