# Simple Maths Question - Capital Sigma/Pi

I haven't studied math in a long time and am trying to solve a simple first order non-homogeneous recurrence relation. This approach uses the general formula:

$$f(n) = \prod_{i=a+1}^n b(i) \bigg\{ f(a) + \sum_{j = a+1}^nd(j)\bigg\}.$$

The recurrence relation itself is

$$f(n) = 6f(n-1) -5; (n > 0)$$

Therefore, $b(i) = 6, f(a) = 2, a = 0, d(j) = -5/6.$

I am a little rusty with maths so am not too confident of the ordering of the calculations.

My attempt:

Calculate

$$\sum_{j = a+1}^nd(j)$$

So $(n - (a+1) + 1) . d(j) = -5/6n$.
Add $f(a)$ to get $2 - 5/6n$. Now sub into general equation:
$\prod_1^n 6(2 - 5/6n)$. I'm not sure how to do this...

The next part is where I am unsure - I'm not entirely sure what the brackets mean after $b(i)$. Could someone help me work through this...I HAVE to use the above formula...

Here is the screenshot from my notes:

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