I love factorials!

Algebra Level 1

Determine the value of n.


The answer is 10099.

Mardokay Mosazghi by Mardokay Mosazghi , 22, USA

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3 solutions

99 ! 101 ! − 99 ! = 99 ! 101 ( 100 ) ( 99 ! ) − 99 ! = 99 ! 99 ! ( 101 ( 100 − 1 ) ) = 1 10100 − 1 = 1 10099 \frac { 99! }{ 101!-99! } =\frac { 99! }{ 101(100)(99!)-99! } =\frac { 99! }{ 99!(101(100-1)) } =\frac { 1 }{ 10100-1 } =\frac { 1 }{ 10099 } , it is a matter of factoring.

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99!/(101!-99!) = 1/(100*101 -1) = 1/(10099)

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Bùi Trí
Dec 1, 2014

99 ! 101 ! − 99 ! \frac{99!} {101!-99!} = 1 n \frac{1} {n} ⇒ 99 ! 101 ( 100 ) ( 99 ! ) − 99 ! \frac{99!} {101(100)(99!)-99!} = 1 n \frac{1} {n} ⇒ 99 ! 99 ! \frac{99!} {99!} ( 1 101 ( 100 ) − 1 \frac{1} {101(100)-1} ) = 1 n \frac{1} {n} ⇒ 1 10100 − 1 \frac{1} {10100-1} = 1 n \frac{1} {n} ⇒ n = 10100 − 1 n = 10100 - 1 ⇒ n = 10099 n = 10099

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