Induction question (1 Viewer)

[shredinator]

Prove 5² >= 4² + 3² for n >= 1

Cheers

 

[nubix]

I'm not that great at maths, but where's the n?

25 = 16 + 9? o.o

 

[Mattamz]

Maybe meant to be:

Prove 5^n >= 4^n + 3^n for n >= 2

Test n=2;
LHS = 25 RHS = 19 + 9 = 25

Assume for n=k;
5^k >= 4^k + 3^k

Prove for n = k + 1;
5^(k+1) >= (4^k+3^k)*5
>= 5*4^k + 5*3^k
>= 4*4^k + 3*3^k
>= 4^(k + 1) + 3^(k+1)

ie if it is true for n =k, it is true for n = k +1