Question 0501c

Sigma Notation
Method of Differences III

Question

Given that f(0)=5,{f(0)=5,} f(1)=2{f(1)=2} and f(2)=8,{f(2)=8,} express
r=1n(2ur+1+ur+ur1)\sum_{r=1}^n \Big( - 2 u_{r+1} + u_r + u_{r-1} \Big)
in the form
a+bun+cun+1,a + bu_n + cu_{n+1},
where a,b{a, b} and c{c} are constants.

Attempt

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

Answer

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