shredinator
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- Feb 4, 2006
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- HSC
- 2007
Prove 52 >= 42 + 32 for n >= 1
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Induction question (1 Viewer)
- Thread starter shredinator
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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
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