Solve the following recurrence relation:
a(n) = a(n-1) + 3(n-1), a(0) = 1
I know this should not be a difficult problem, but my main problem is in solving the problem when the coefficient of the a(n-1) term is 1. Also, when a summation is in the solution, I do not understand how to convert from a summation to a C(n,k) or a P(n,k). Could you please give a step by step explanation of the process involved with solving this type of problem? Thank you.© BrainMass Inc. brainmass.com November 24, 2022, 11:46 am ad1c9bdddf
a(1) = a(0) + 0 = 1
a(n) = a(n-1) + 3*(n-1).....
a(n) = a(n-2)+3*(n-2)+ 3*(n-1).....
a(n)= a(n-3) + 3*(n-3) + 3*(n-2) + 3*(n-1).....
and so on till u get a(1)...
So u will have:
a(n) = a(1) + 3*(1+2+3+4........+n-1)
Now sum of first k numbers is k(k+1)/2
with k=n-1 in this case.
so a(n) = 1 + [3*n(n-1)/2]
THIS IS THE SIMPLEST KIND OF RECURRENCE ...
A recurrence relation is solved. The solution is detailed.