document.write( "Question 25077: What is the product of the first 99 products in the sequence 1/2 2/3 3/4 4/5...? \n" ); document.write( "

Algebra.Com's Answer #13454 by askmemath(368) $\"\"$ $\"About$

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Consider only the first 2 terms $\"1%2F2+%2A+2%2F3\"$
\n" ); document.write( "The 2 in the Numerator and Denominator cancel leaving you with only $\"1%2F3\"$
\n" ); document.write( "Expand this to 3 terms $\"1%2F2+%2A+2%2F3+%2A+3%2F4\"$
\n" ); document.write( "The 2 and 3 will cancel leaving you out with $\"1%2F4\"$
\n" ); document.write( "You will observe that as we increase the number of terms, the denominator increases by 1 everytime
\n" ); document.write( "So for 99 terms the denominator increasing by 1 will give us 100
\n" ); document.write( "And so your answer will be $\"1%2F100\"$ \n" ); document.write( "

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