Find a positive value of m for which the coefficient of x² in the expansion

(1 + x)^m is 6.

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Solution

It is known that (r + 1)^th term, (T_r₊₁), in the binomial expansion of (a + b)ⁿ is given by .

Assuming that x² occurs in the (r + 1)^th term of the expansion (1 +x)^m, we obtain

Comparing the indices of x in x² and in T_r_{+ 1}, we obtain

r = 2

Therefore, the coefficient of x² is.

It is given that the coefficient of x² in the expansion (1 + x)^m is 6.

Thus, the positive value of m, for which the coefficient of x² in the expansion

(1 + x)^m is 6, is 4.

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