Hey,
I have a question about creating functions:
Given \(\displaystyle \displaystyle f(x)\, =\, \sum_{i = 0}^{\infty}\, a_i\, x^i ,\) that \(\displaystyle f(x)\, (1\, +\, 2x\, +\, 2x^2\, +\, x^3)\, =\, \dfrac{1}{(1\, -\, x)^3}\)
1. I am right that: a0=1, a1=2, a2=2?
2. We need to find numbers - r, s, t, so that - \(\displaystyle a_n\, =\, D(3,\, n)\, -\, r\, a_{n-1}\, -\, s\, a_{n-2}\, -\, t\, a_{n-3}\), for all 3≤n. Think of a7 using this formula.
To question 2 I need the start of the solution if possible please
Thanks
I have a question about creating functions:
Given \(\displaystyle \displaystyle f(x)\, =\, \sum_{i = 0}^{\infty}\, a_i\, x^i ,\) that \(\displaystyle f(x)\, (1\, +\, 2x\, +\, 2x^2\, +\, x^3)\, =\, \dfrac{1}{(1\, -\, x)^3}\)
1. I am right that: a0=1, a1=2, a2=2?
2. We need to find numbers - r, s, t, so that - \(\displaystyle a_n\, =\, D(3,\, n)\, -\, r\, a_{n-1}\, -\, s\, a_{n-2}\, -\, t\, a_{n-3}\), for all 3≤n. Think of a7 using this formula.
To question 2 I need the start of the solution if possible please
Thanks
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