DO IT ASAP I HAVE NO TIME I WILL VOTE PLEASEEEE

Suppose you want to use mathematical induction to prove that 1 + 2 + 3+...+1 for all positive integers n. Which of these is the correct implication P(1) - P(k+ 1) to be used in the inductive step? Select one 19+27+3+...+2+1 +2 +3+...+n + (n + 1)? O 11? (n + 1)' 1 + 2 + 3+...+n? - R(!)(2011) 41 +2 +3+ + + (n+1) = 12:11 +(n+1) Od 1+22+3+...+n? tai 1 (2011) +1 +2 +32+... +n + (n + 1)2 = (0 : 1) 42)(2014-2) Assume that you are using linear search algorithm to find the position of elementx-9 In the list L-{1,2,3,4,5,6,7,8,9,10). What is the number of comparisons done by the algorithm until it finds the position of x? (Include all comparisons in your countl) Linear search algorithm is given as: procedure linear search(x:integer, a, .....,:distinct integers) 1:-1 while (I s n and xal iris n then location : else location : 0 return location Select one: O a. 10 O 1.9 O c. 19 O d. 18 How many non-zero entries does the matrix representing the relation Ron A = {1,2,3,..., 30) consisting of the first 30 positive Integers have if Ris((a,b)|(a > b) or (b>a))? Select one: O a. 30 O b: 900 O c.450 O d. 870 How many students must be in a class to guarantee that at least 5 students receive same score on the final exam. If the exam is graded on a scale from 0 to 100 points? Select one: O a 404 O 6.505 O c504 d. 405 What is the smallest integer n for which the function f(x)-[x+1)(x+2)(x+2)+x[x?+7) is 0(x")? Select one: O an=7 O b.n=4 O cn=6 dn=5