ANSWER 2-6 PLEASE PLEASE PLEASE!!!!

2. (5 points) for what values of n is mac{f(n), o(f(n))} = f(n) true? Assume f(n) is asymptotically positive

3. Say g(n) = (f(n)). Which of the following is true? Assume g and f are asymptotically positive.

4. When is f(n) O(f(n/2))?

5. Fill in the blank. f(n)=(g(n)) if and only if g(n) = ____(f(n)).

6. Consider the sum E (n+3)/(n(n+1)) * ()^n

a. Which of the following partial fractions equals (n+3)/(n(n+1))?

b. Which of the following series can be used to evaluate the sum?

2. (5 points) For what values of n is mar{f(n), f(n))} = f(n) true? Assume f(n) is asymptotically positive. A. only for small values of n B. only when n is sufficiently large C. never D. always 3. (5 points) Say g(n) = e(f(n)). Which of the following is true? Assume , and f are asymptotically positive. A. g(n)/f(n) - constant for all sufficiently large n B. g(n)-1(f(n/2)) C. g(10) S 101000f(n) D. *) = 0(en)) 1. (5 points) When is f(n) +0(f(n/2))? A. when f(n) is polynomial B. when f(n) is exponential C. never D. always 5. (5 points) Fill in the blank. f(n) = (g(n)) if and only if g(n)=__(f(n)). A. O B. w C. D. none of the above ()" 6. (10 points) Consider the sum +3 n(n+1) a. (2 points) Which of the following partial fractions equals lui? A++ B. + TE c. 1 2 w+I D. none of the above b. (4 points) Which of the following series can be used to evaluate the sum? A. geometric miris B. arithmetic series C. telescoping series