1) Reduce ((n + 1)!)/((n - 2)!) 2) Evaluate the sequence 1(1!)+...+2(2!)+...+n(n

Question

1) Reduce ((n + 1)!)/((n - 2)!) 2) Evaluate the sequence 1(1!)+...+2(2!)+...+n(n!) for n=5 3) If you are given a sequence function f(n) = 4n-1, find the recursive sequence that will give you the same results. 4) Given the recursive sequence a1 = 4, an = an-1 + 3, find the sequence function that will give the same results 1) Reduce ((n + 1)!)/((n - 2)!) 2) Evaluate the sequence 1(1!)+...+2(2!)+...+n(n!) for n=5 3) If you are given a sequence function f(n) = 4n-1, find the recursive sequence that will give you the same results. 4) Given the recursive sequence a1 = 4, an = an-1 + 3, find the sequence function that will give the same results

Explanation / Answer

1) (n+1)!/(n-2)! = ((n+1)(n)(n-1)(n-2)(n-3)...)/((n-2)(n-3)(n-4)...) Just cross out which ones cancel, and it reduces the expression. 2) You can just do this numerically. 1(1!)=1, 2(2!)=2(2)(1)=4, 3(3!)=3(3)(2)(1)=18, etc. then add them together. 3) For a0=1, a1 = 4a0 -1, a2=8/3a1-1, a3=12/7a2-1, a4=16/11a3-1... look at the pattern in these numbers and figure them out in terms of n. 4) Write them out and look for the pattern, it's usually easier to go from sequence to function than the other way around. a1 = 4, so a2 = a1 + 3 = 7, a3 = a2 + 3 = 10, a4 = a3 + 3 = 13....

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