Please answer the 10th question. I. (2 points) Let F, be the Fibonacci numbers,

Question

Please answer the 10th question.

I. (2 points) Let F, be the Fibonacci numbers, where Fo= l, F,-I, F2-2, F,-3, F. = 5 . Prove -2 F1 = FN-2, where N> 2 using induction. (Lipschutz, HW 3) 2 C2 points) Use induction to prove that fr all natural numbersas divisible by x-1. Heileman, p.415) 3. (2 points) Prove by induction that l 2 + 22 + 32 + + n2 4. (2 points) Prove by induction that the sum of the first n odd positive integers is n, i.e., 1 +3+5 (2n)-r 5, (2 points) Prove that -ok2k-(n-1)2n+1 + 2. (Heileman, p. 415) 6. (2 points) Assuming a and b are arbitrary constants, and 0

Explanation / Answer

O(g(n))=f(n) such that there exsits a postitve constant c and so 0<=f(n) <= c*g(n)

to prove

O(logn)=log(n+1)  

we have to show that there exsits a postitve constant c and so zero(0)<=log(n+1) <= c*logn

so if c=100 clearly 0<=log(n+1)<=100logn

hence proved

O(logn)=log(n+1)  

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---