Easy Telescoping Factorial Sum

Algebra Level 3

x=101!×(12!+23!+34!++99100!) x = 101! \times \left(\frac{1}{2!} + \frac{2}{3!} + \frac{3}{4!} +\cdots+ \frac{99}{100!}\right)

Find 101!x. 101! - x .

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