It doesn't even matter! (But what?)

Probability Level 2

( 1729 0 ) − ( 1729 1 ) + ( 1729 2 ) − . . . . + ( − 1 ) 1729 ( 1729 1729 ) = ? {1729\choose 0}-{1729 \choose 1}+{1729 \choose 2}-....+{ \left( -1 \right) }^{ 1729 }{1729 \choose 1729}=?

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The answer is 0.

Shivamani Patil by shivamani patil , 21, India

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1 solution

Pranjal Jain
May 1, 2015

( 1 + x ) 1729 = ( 1729 0 ) + ( 1729 1 ) x + ( 1729 2 ) x 2 + ⋯ + ( 1729 1729 ) x 1729 (1+x)^{1729}={1729\choose 0}+{1729 \choose 1}x+{1729 \choose 2}x^2+\cdots+{1729 \choose 1729}x^{1729}

Substitute x = − 1 x=-1

( 1729 0 ) − ( 1729 1 ) + ( 1729 2 ) − . . . . + ( − 1 ) 1729 ( 1729 1729 ) = 0 {1729\choose 0}-{1729 \choose 1}+{1729 \choose 2}-....+{ \left( -1 \right) }^{ 1729 }{1729 \choose 1729}=0

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Correct.Try this here

shivamani patil - 6 years, 1 month ago

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