Prove by Mathematical Induction that for .
Step 1: Prove true for n = 1
hence true for n = 1
Step 2: Assume true for n = k
Step 3: Prove true for n = k + 1
not really sure what to do from here, tried this approach
since from step 2 we know that , but not sure if this is right as I do not know what to do with the 2k - 10
any insight appreciated
thanks for that,
Wasnt sure if you could use that type of approach, or if it was thought of as a sort of cheat way around.
I did try
using the discriminant :
but that proves that it is not positive definite (which is what i would have expected), it has two distinct rational roots, so it would NOT be larger than or equal to 0 for all k since it is indefinite, unless something is dodgy with my logic here