What makes a number binomial? Generalizing the binomial theorem

Probability Level 1

Expand ( a + b ) n (a+b)^{n} .

( n 0 ) a n + ( n 1 ) a n − 1 b + . . . + ( n n ) b n \binom{n}{0}a^{n} + \binom{n}{1}a^{n-1}b + ... +\binom{n}{n}b^{n} ∑ i = 1 n ( − 1 ) n ( n i ) a i b n − i \sum_{i = 1}^{n}(-1)^{n}\binom{n}{i}a^{i}b^{n-i} ( n 0 ) a n − ( n 1 ) a n − 1 b + . . . + ( − 1 ) n ( n n ) b n \binom{n}{0}a^{n} - \binom{n}{1}a^{n-1}b + ... +(-1)^{n}\binom{n}{n}b^{n} Not possible to generalize

Sanchayapol Lewgasamsarn by Sanchayapol Lewgasamsarn , 20, Thailand

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1 solution

Atul Kumar
Jun 17, 2014

just a simple application of binomial theorem : (a+b)^n=nC0.a^n+nc1.a^n-1.b+......+nCn.b^n

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