# What's the maths symbol for alternation of product and sums?

Is there a mathematics symbol for referring to the equation below?

(((((((((((100*y-x) *y-x) *y-x) *y-x) *y-x) *y-x) *y-x) *y-x) *y-x) *y-x) *y-x) *y-x = 0, x = 9.8

I've tried using capital sigma and capital PI but both of them can't seem to be able to express the above equation.

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## 1 Answer

Depending on your context and needs you can either view it as iteration of a function: $$f^{12}(100) \qquad\text{where }f(z)=zy-x$$

or you can apply the distributive law and get $$100y^{12} - xy^{11} - xy^{10} - \cdots - xy^2 - xy - x$$

which after a bit more rearrangement becomes $$100y^{12} - x\frac{y^{12}-1}{y-1}$$

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Do you happen to know how we can type f12(100) where f(z) = zy - x; x = 9.8 into wolfram alpha to solve for y? – Pacerier Dec 14 '13 at 5:34
@Pacerier: No.  – Henning Makholm Dec 14 '13 at 6:24
@Pacerier use the Nest command. WA accept something like "Solve[ Nest[y*#-9.8 &,100,12] == 0, y]" and give you this – achille hui Dec 14 '13 at 7:29