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If the value of sum of first 7 non-zero natural numbers is equal to 8!𝑥448!x​ , then find the value of 1𝑥x1​ ?

Question

If the value of sum of first 7 non-zero natural numbers is equal to 8!×448! 8! \times 448! , then find the value of 1×x×1 1 \times x \times 1 .

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Solution

The sum of first 7 non-zero natural numbers is 1+2+3+4+5+6+7 = 28.

Given that 28 = 8! * x * 448! * x

We can simplify this equation by cancelling out the common factors.

First, note that 8! = 40320 and 448! is a very large number. However, we can simplify this equation by noting that 28 is a factor of both 8! and 448!.

So, we can divide both sides of the equation by 28 to get:

1 = 8! * x * 448! * x / 28

Solving for x, we get:

x = sqrt(1 / (8! * 448! / 28))

Now, we need to find the value of 1/x.

1/x = sqrt(8! * 448! / 28)

So, the value of 1/x is the square root of the product of 8! and 448! divided by 28.

This problem has been solved

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