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Algebra Level 3

1 99 ! + 1 2 ! × ( 98 ! ) + 1 3 ! ( 97 ! ) . . . . . . . . . . . . . 1 100 ! = ( 2 n ) − 1 n ! \dfrac{1}{99!} +\dfrac{1}{2! \times (98!)} + \dfrac{1}{3!(97!)} .............\dfrac{1}{100!} =\dfrac{( 2^ n) -1}{n!}

What is the value of n n ?


The answer is 100.

U Z by U Z , 24, Guyana

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1 solution

U Z
Sep 16, 2014

general term = 1/(100 - k )! (k!) then multiplying and dividing by 100! it becomes 100Ck /100! their sum is 2^100 - 1/100!

2 Helpful 0 Interesting 0 Brilliant 0 Confused

The term in the question should be (2^n -1)/n!. The question doesn't have the factorial sign "!" after the "n".

Siddhartha Srivastava - 6 years, 8 months ago

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sorry true

U Z - 6 years, 8 months ago

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