But there's a hundred terms!

Algebra Level 1

( 50 − 1 ) ( 50 − 2 ) ( 50 − 3 ) ⋯ ( 50 − 99 ) ( 50 − 100 ) = ? \large (50-1)(50-2)(50-3)\cdots(50-99)(50-100) = \ ?


The answer is 0.

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Raghu Raman Ravi by Raghu Raman Ravi , 20, India

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4 solutions

Vivek Kumar
Aug 14, 2014

(50-1)(50-2)(50-3).......(50-50)..............(50-99)(50-100)

since all are in product form and 50 - 50 is 0

2 Helpful 0 Interesting 0 Brilliant 0 Confused

50!/[100!*(50-100)!] = 0

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Ritam Baidya
Dec 3, 2014

in between we get(50-50) = 0 so the whole expression gets multiplied by 0 and so the answer is also 0

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Raghu Raman Ravi
Aug 12, 2014

since 50-50=0 the whole product is 0

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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