Question

Find the numerically greatest term in the expansion of (3-2x)^9 when x=1

Answer 1

Answer:

Step-by-step explanation:

Find the greatest term in the expansion of (3-2x)^9 when x = 1.

Solution:

     Tr+1 / Tr = ((9-r+1)/r) . (2x/3) >1

    i.e. 20 > 5r

If r = 4, then Tr+1 = Tr and these are the greatest terms. Thus 4th and 5th terms are numerically equal and greater than any other term and their value is equal 3^9 × 9C3 × (2/3)^3 = 3^6 x 8 x (9.8.7.6!)/3!.6! =  3^6 x 8 x 3.7.4 =  489888.