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\frac{a}{c} + \frac{bc - ad}{c} \left [ \frac{(cx - a + \alpha)\alpha^{n - 1} - (cx - a + \beta)\beta^{n - 1}}{(cx - a + \alpha)\alpha^{n} - (cx - a + \beta)\beta^{n}} \right ]
where:

\alpha = \frac{a + d + \sqrt{(a - d)^2 + 4bc}}{2}
\beta = \frac{a + d - \sqrt{(a - d)^2 + 4bc}}{2}

\left\{b+1,\sum_{i=a}^b g(i)\right\} \equiv \left( \{i,x\} \rightarrow \{ i+1 ,x+g(i) \}\right)^{b-a+1} \{a,0\}
and the equivalent product:

\left\{b+1,\prod_{i=a}^b g(i)\right\} \equiv \left( \{i,x\} \rightarrow \{ i+1 ,x g(i) \}\right)^{b-a+1} \{a,1\}

 Jul 2, 2014

Best Answer 

 #1
avatar+33665 
+5

You need to select the LaTeX Formula button from the ribbon and enter your LaTeX into that (I just copied and pasted it below).  

$$\frac{a}{c} + \frac{bc - ad}{c} \left [ \frac{(cx - a + \alpha)\alpha^{n - 1} - (cx - a + \beta)\beta^{n - 1}}{(cx - a + \alpha)\alpha^{n} - (cx - a + \beta)\beta^{n}} \right ]
where:

\alpha = \frac{a + d + \sqrt{(a - d)^2 + 4bc}}{2}
\beta = \frac{a + d - \sqrt{(a - d)^2 + 4bc}}{2}

\left\{b+1,\sum_{i=a}^b g(i)\right\} \equiv \left( \{i,x\} \rightarrow \{ i+1 ,x+g(i) \}\right)^{b-a+1} \{a,0\}
and the equivalent product:

\left\{b+1,\prod_{i=a}^b g(i)\right\} \equiv \left( \{i,x\} \rightarrow \{ i+1 ,x g(i) \}\right)^{b-a+1} \{a,1\}$$

I'm not clear what your question is though!

 Jul 2, 2014
 #1
avatar+33665 
+5
Best Answer

You need to select the LaTeX Formula button from the ribbon and enter your LaTeX into that (I just copied and pasted it below).  

$$\frac{a}{c} + \frac{bc - ad}{c} \left [ \frac{(cx - a + \alpha)\alpha^{n - 1} - (cx - a + \beta)\beta^{n - 1}}{(cx - a + \alpha)\alpha^{n} - (cx - a + \beta)\beta^{n}} \right ]
where:

\alpha = \frac{a + d + \sqrt{(a - d)^2 + 4bc}}{2}
\beta = \frac{a + d - \sqrt{(a - d)^2 + 4bc}}{2}

\left\{b+1,\sum_{i=a}^b g(i)\right\} \equiv \left( \{i,x\} \rightarrow \{ i+1 ,x+g(i) \}\right)^{b-a+1} \{a,0\}
and the equivalent product:

\left\{b+1,\prod_{i=a}^b g(i)\right\} \equiv \left( \{i,x\} \rightarrow \{ i+1 ,x g(i) \}\right)^{b-a+1} \{a,1\}$$

I'm not clear what your question is though!

Alan Jul 2, 2014

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