For every integer n ≥ 1 , ( 0 n ) − ( 1 n ) + ( 2 n ) − ... + ( − 1 ) n ( n n ) = 0.
(Hint: Use the fact that 1 + ( − 1 ) = 0. )
To show that for every integer n≥1 ,
(n0)−(n1)+(n2)−…+(−1)n(nn)=0.
Given information:
Use the fact that 1+(−1)=0.
Formula used:
Binomial theorem:
(a−b)n=( n 0 )an(−b)0+( n 1 )an−1(−b)1+( n 2 )an−2(−b)2+( n 3 )an−3(−b)3 +.........+( n n−1 )a1(−b)n−1+( n n )a0(−b)n
Proof:
1+(</
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