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Home » If the coefficients of (2r + 4)th and (r – 2)th terms in the expansion of (1 + x)18 are equal, find r.
If the coefficients of (2r + 4)th and (r – 2)th terms in the expansion of (1 + x)18 are equal, find r.
Binomial Theorem | CBSE | Class 11 | Exercise 18.2 | Maths | RD Sharma
If the coefficients of (2r + 4)th and (r – 2)th terms in the expansion of (1 + x)18 are equal, find r.

Answer:

Coefficient of the r term in the expansion of (1 + x)n is nCr-1

Coefficients of the (2r + 4) and (r – 2) terms in the given expansion are 18C2r+4-1 and 18Cr-2-1

Equaling two coefficients,

18C2r+4-1 = 18Cr-2-1

18C2r+3 = 18Cr-3

2r + 3 = r – 3 or 2r + 3 + r – 3 = 18  [nCr = nCs => r = s (or) r + s = n]

2r – r = -3 – 3 or 3r = 18 – 3 + 3

r = -6 or 3r = 18

r = -6 or r = 18/3

r = -6 or r = 6

∴ r = 6

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