The numerically greatest term in the binomial expansion of (2 a-3 b)¹⁹ when a= 1 4 and b= 2 3 is

Step-by-step solution

We have, (2 a-3 b)¹⁹=2¹⁹ a¹⁹ (1- 3 b 2 a )¹⁹ Ne know that, the r^ th term of greatest term of aligned (1+x)^n & = [ (n+1)|x| 1+|x| ] n & =19, x=- 3 b 2 a aligned Here, n=19, x=- 3 b 2 a r= [ (20) | 3 b 2 a | 1+ 3 b 2 a ]= [ 20 1+4 4 ] [ b= 2 3 , a= 1 4 ] r=16 greatest term of (2 a-3 b)¹⁹ is aligned & = 19 16 2¹⁹ a¹⁹ ( 3 b 2 a )¹⁶ & = ¹⁹ C₃ 2¹⁹ ( 1 4 )¹⁹ (4)¹⁶ [ 19 16 = ¹⁹ C₃ ] & = ¹⁹ C₃ 2¹⁹ 1 2³⁸ 2³²= ¹⁹ C₃ 2¹³ aligned