Question

Вычислить(1-1/4)(1-1/9)(1-1/16)(1-1/25)...(1-1/9801)(1-1/10000)​

Answer 1

Ответ:

вот☝️

Объяснение:

вроде так нашла в инете

Answer 2

The expression you're asking to calculate is the product of a series of terms in the form $1 - \frac{1}{n^2}$ for various values of $n$. We can rewrite each term as $\frac{n^2 - 1}{n^2}$, and notice that each term cancels out nicely:

$$\begin{align*} & (1 - \frac{1}{4})(1 - \frac{1}{9})(1 - \frac{1}{16}) \ldots (1 - \frac{1}{9801})(1 - \frac{1}{10000}) \\ & = \left(\frac{3}{4}\right) \left(\frac{8}{9}\right) \left(\frac{15}{16}\right) \ldots \left(\frac{9800^2}{9801^2}\right) \left(\frac{9999^2}{10000^2}\right) \\ & = \frac{3 \times 8 \times 15 \times \ldots \times 9800^2 \times 9999^2}{4 \times 9 \times 16 \times \ldots \times 9801^2 \times 10000^2} \\ & = \frac{(3 \times 8 \times 15 \times \ldots \times 9800 \times 9999)(3 \times 8 \times 15 \times \ldots \times 9800 \times 9999)}{(4 \times 9 \times 16 \times \ldots \times 9801 \times 10000)(4 \times 9 \times 16 \times \ldots \times 9801 \times 10000)} \\ & = \frac{(9999! \times 9999!)}{(10000! \times 10000!)} \\ & = \frac{1}{10000} \end{align*}$$

So, the product is $\frac{1}{10000}$.