Find numerically the greatest term in the expansion of (2 + 3x)^9 , where x = 3/2 .

Question

Find numerically the greatest term in the expansion of (2 + 3x)⁹ , where x = \(\frac{3}{2}\).

Answer 1

To Find : numerically greatest term

For (2+3x)⁹ ,

a=2, b=3x and n=9 

We have relation,

t_r+1 ≥ t_r or \(\frac{t_{r+1}}{t_r}\) ≥ 1

We have a formula,

Conclusion : the 7^th term is numerically greater with value (₂⁹) 2² (3)⁷(X)⁷