Question 0501c

Sigma Notation
Method of Differences III

Question

Given that f(0)=2,{f(0)=2,} f(1)=3{f(1)=3} and f(2)=1,{f(2)=1,} express
r=1n(f(r+1)3f(r)+4f(r1))\sum_{r=1}^n \Big( - f(r+1) - 3 f(r) + 4 f(r-1) \Big)
in the form
a+bf(n)+cf(n+1),a + bf(n) + cf(n+1),
where a,b{a, b} and c{c} are constants.

Attempt

a={a=}
b={b=}
c={c=}

Answer

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