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$\begin{cases} f(1)=15 \ f(n)=f(n-1) \cdot n \end{cases}$

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Estimate customary measurements

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Q.

\begin{cases} f(1)=15 \ f(n)=f(n-1) \cdot n \end{cases}

Understand Recursive Function: To solve the problem, we need to understand the recursive function given. The function $f(n)$ is defined such that the value of $f(n)$ is the product of $n$ and the value of $f$ at $n-1$ , i.e., $f(n-1)$ . The base case is given as $f(1) = 15$ .
Calculate $f(2)$ : Let's calculate the value of $f(2)$ using the recursive formula. According to the formula, $f(2) = f(2-1) \times 2 = f(1) \times 2$ . We know that $f(1) = 15$ , so $f(2) = 15 \times 2 = 30$ .
Calculate $f(3)$ : Next, we calculate the value of $f(3)$ . Using the recursive formula, $f(3) = f(3-1) \times 3 = f(2) \times 3$ . We found that $f(2) = 30$ , so $f(3) = 30 \times 3 = 90$ .
Calculate $f(4)$ : To find the value of $f(4)$ , we use the recursive formula again: $f(4) = f(4-1) \times 4 = f(3) \times 4$ . We have already calculated $f(3) = 90$ , so $f(4) = 90 \times 4 = 360$ .
Continue Recursive Process: The pattern is clear, and we can continue this process to find $f(n)$ for any positive integer $n$ . However, without a specific value of $n$ , we cannot calculate an exact value for $f(n)$ . We can only describe the process.

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