Find the coefficient of a5 b7 in a-2 b12

It is known that (r + 1)th term, (Tr+1), in the binomial expansion of (a + b)n is given by . Assuming that a5b7 occurs in the (r + 1)th term of the expansion ( ...

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Standard XII

Mathematics

Higher Order Derivatives

Find the coef...

Question

Find the coefficient of a⁵b⁷ in (a – 2b)¹²

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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 a⁵b⁷ occurs in the (r + 1)^th term of the expansion (a – 2b)¹², we obtain

Comparing the indices of a and b in a⁵ b⁷and in T_r₊₁, we obtain

r = 7

Thus, the coefficient of a⁵b⁷ is

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Find the coefficient of a5b7 in (a – 2b)12

It is known that (r + 1)th term, (Tr+1), in the binomial expansion of (a + b)n is given by . Assuming that a5b7 occurs in the (r + 1)th term of the expansion (a – 2b)12, we obtain Comparing the indices of a and b in a5 b7 and in Tr +1, we obtain r = 7 Thus, the coefficient of a5b7 is

Find the coefficient of a⁵b⁷ in (a – 2b)¹²