Answer:

Coefficient of the r term in the expansion of (1 + x)ⁿ – ⁿC_r-1

Coefficients of the (2r + 1) and (r + 2) terms in the given expansion are ⁴³C_2r+1-1 and ⁴³C_r+2-1

Equaling two coefficients,

⁴³C_2r+1-1 = ⁴³C_r+2-1

⁴³C_2r = ⁴³C_r+1

2r = r + 1 or 2r + r + 1 = 43 [ ⁿC_r = ⁿC_s => r = s (or) r + s = n]

2r – r = 1 or 3r + 1 = 43

r = 1 or 3r = 43 – 1

r = 1 or 3r = 42

r = 1 or r = 42/3

r = 1 or r = 14

∴ r = 14