Re: If k = 10!(1 + 1/2 + 1/3 + 1/4 + 1/5....
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01 Sep 2022, 04:37
First, simplify the expression:
1+ 1/2 + ... + 1/10 to S / 2520, where S is some number and 2520 is the LCM of the denominators of the above expression.
However, 2520 = 10x7x9x2x2.
Then, the expression in the question can be written as:
10!(S)/10x7x9x2x2.
This is equivalent to:
10x9x8x...x1 (S) / 10x7x9x2x2.
After cancelling out 10, 7, 9 and 4 from the numerator, the numerator becomes : 8x6x5x3x2 * S. The denominator is 1.
This above number can be divided by each of the answer choices except 7. Hence, answer is C.