TheMathWorld

Question-70 Prove that 3n < n! if n is an integer greater than 6. The basis step is n = ?. The basis step is true since ?  <  ?…

Question-69 a) Find a formula for  By examining the values of this expression for small values of n. The formula for the sum is ?   b)  Prove the formula…

Question-68 Let P(n) be the statement that 13  + 23  + …. + n3 = for the positive integer n. a)     What is the statement P(1) ? P(1) is the…

Question-67 What is the largest n for which one can solve within one second using an algorithm that requires f(n) bit operations, where each bit operation is carried out in…

Question-66 How much time dose an algorithm take to solve a problem of size n if this algorithm uses operations, each requiring second, with the following values of n ?…

Question-65 What is the largest n for which one can solve within one second a problem using an algorithm that requires f (n) bit operations, where each bit operations, where…

Question-64  There is a more efficient algorithm (in terms of the number of multiplications and additions used) for evaluating polynomials than the conventional algorithm. It is called Horner’s method. This…

Question-63 Give a  big-O estimate for the number of comparisons used by the algorithm that determines the number of 1 s in a bit string n by examining each bit…

Question-62 Give a big-O estimate for each of the following function. For the function g in the estimate f (x) is O (g(x)) , use a simple function g of…

Question-61 Let k be a positive integer. Which of the following mathematical equations correctly shows that 1k + 2k + ………….  + nk  is O ?   Solution