The greatest binomial coefficient in ( 1 + x ) 40 + m is ∑ i = 0 m ( i m ) ( m − i 40 ) , where m is an even natural number. Find m .

Question

The greatest binomial coefficient in ( 1 + x ) 40 + m is ∑ i = 0 m ​ ( i m ​ ) ( m − i 40 ​ ) , where m is an even natural number. Find m .

TestHub · Accepted Answer

Vandermonde gives the sum as ( m 40 + m ​ ) . The greatest coefficient of ( 1 + x ) 40 + m is the middle term ( 20 + m /2 40 + m ​ ) . Equality gives 20 + m /2 = m , so m = 40 .

Mathematics - Binomial Theorem Question with Solution | TestHub

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