Question

find the third term in expansion of (2x^2 + 3/2x)^8. In this question of mathematical induction, how do I find r ?

Answer 1

Solution........

Third Expansion of (2x^2 + 3/2x)^8 :-

t3 = 8C2 × (2x^2)^8-2 × (3/2x)^2
= 8C2 × (2x^2)^6 × 9/4x^2
= 8C2 × 2^6 × x^8 × 9/4x^2
= 8C2 × 64 × 9/4 × x^8/x^2
= 8C2 × 16 × 9 × x^6
= 8C2 × 144 × x^6
= [(8×7) ÷ 2] × 144 × x^2
= 4×7 × 144 × x^2
= 4032 x^2.

Therefore, third term of the Expansion is 4032x^2.

☞ To find r, ➡ The subtract 1 from the given term. [ like 3 is the given term so, (3-1 = 2 = r ) ].

Hope this will help you......

☞ ☆☆ @ Mr. Thakur ☆☆