F.4 (x+1)^29

(x + 1)^29 = x^29 + C(29, 1)x^28 + C(29, 2)x^27 + ...... + C(29, 28)x +1

Coefficient of the Rth term = C(29, R-1)
Coefficient of the (R+1)th term = C(29, R)

C(29, R-1) : C(29, R) = 3 : 2
29!/(R-1)![29-(R-1)]! : 29!/R!(29-R)! = 3 : 2
1/(R-1)!(30-R)! : 1/R!(29-R)! = 3 : 2
1/(R-1)!(30-R)(29-R)! : 1/R(R-1)!(29-R)! = 3 : 2
1/(30-R) : 1/R = 3 : 2
2 * [1/(30-R)] = 3 * (1/R)
2/(30-R) = 3/R
2R = 3(30-R)
2R = 90-3R
5R = 90
R = 18