For every integer n ≥ 0 , ∑ i = 0 n ( − 1 ) i ( i n ) 3 n − i = 2 n .
To prove that for every integer n≥0 ,
∑i=0n(−1)i(ni)3n−i=2n
Given:
The integer n≥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:
2=3−12n=[3−1
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