Find the 5th term in the expansion of (3x – 1/x2)10.

1.	Find the 5th term in the expansion of (3x – 1/x2)10.
Answer» Given as (3x – 1/x²)¹⁰ Now, the 5^th term from the end is the (11 – 5 + 1)th, is., 7^th term from the beginning. Therefore, T₇ = T₆₊₁ = ¹⁰C₆ (3x)^10-6 (-1/x²)⁶ = ¹⁰C₆ (3)⁴ (x)⁴ (1/x¹²) = [10 × 9 × 8 × 7 × 81] / [4 × 3 × 2 × x⁸] = 17010 / x⁸ Thus, the 5^th term of the expression (3x – 1/x²)¹⁰ is 17010 / x⁸.

Answer»

Given as

(3x – 1/x²)¹⁰

Now, the 5^th term from the end is the (11 – 5 + 1)th, is., 7^th term from the beginning.

Therefore,

T₇ = T₆₊₁

= ¹⁰C₆ (3x)^10-6 (-1/x²)⁶

= ¹⁰C₆ (3)⁴ (x)⁴ (1/x¹²)

= [10 × 9 × 8 × 7 × 81] / [4 × 3 × 2 × x⁸]

= 17010 / x⁸

Thus, the 5^th term of the expression (3x – 1/x²)¹⁰ is 17010 / x⁸.

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