I have a small algebra problem

If the sum of two consecutive integers is $x$, what would be their product?

I've made equation.$$n+(n+1)=x$$

But, don't understand how to find their sum.

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# [Math] Product of two consecutive integers.

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algebra-precalculuslinear algebra

I have a small algebra problem

If the sum of two consecutive integers is $x$, what would be their product?

I've made equation.$$n+(n+1)=x$$

But, don't understand how to find their sum.

## Best Answer

$$n + (n + 1) = x \implies n = \frac{x - 1}{2}$$

Then $$n(n + 1) = \left(\frac{x - 1}{2}\right) \left(\frac{x - 1}{2} + 1\right) = \left(\frac{x - 1}{2}\right)\left(\frac{x + 1}{2}\right) = \frac{x^2 - 1}{4}.$$