# What is the product of $\frac{3}{2} \times \frac{4}{3} \times \frac{5}{4} \ldots \times \frac{2006}{2005}$?

Question

What is the product of $\frac{3}{2} \times \frac{4}{3} \times \frac{5}{4} \ldots \times \frac{2006}{2005}$?

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1 year 2021-09-01T21:40:16+00:00 1 Answers 5 views 0

2.5

Step-by-step explanation:

We need to find the product of the following expression.

$$\dfrac{3}{2}\times \dfrac{4}{3}\times \dfrac{5}{4}\times \dfrac{2006}{2005}$$

3 and 4 are there in both numerator and denominator. It will cancel out.

$$\dfrac{1}{2}\times \dfrac{1}{1}\times \dfrac{5}{1}\times \dfrac{2006}{2005}\\\\=\dfrac{5}{2}\times \dfrac{2006}{2005}\\\\= 2.5$$

So, the value of the above expression is 2.5.