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The numerically greatest term in the expansion of (3-2x)^{9} w

Question

The numerically greatest term in the expansion of $(3 - 2 x)^{9}$ when $x = 1$ is

4th term

5th term

6th term

7th term

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The numerically greatest term in the expansion of

(3 - 2 x)^{9}

when

x = 1

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Text solutionVerified

= (3 - 2 x)^{9}

= 3^{9} (1 - \frac{2 x}{3})^{9}

= 3^{9} (1 - \frac{2}{3})^{9}

let Trt, be the greatest term this exp.

Tr+1

\geq T r

^{9} C_{r} (\frac{- 2}{3})^{r} \geq^{9} C_{r - 1} (\frac{- 2}{3})^{r - 1}

\Rightarrow \frac{9 !}{r ! ∣9 - r ∣ !} (\frac{- 2}{3})^{r - r + 1} \geq \frac{9 !}{( r - 1 )! ∣9 - r + 1∣ !}

\Rightarrow \frac{1}{r ∣ r - 1∣ ! ∣9 - r ∣ !} ∣ ∣ \frac{- 2}{3} ∣ ∣ \geq \frac{1}{( r - 1 )! ( 10 - r ) ( 9 - r )!}

= (- 2 (10 - r)) \geq (3 r)

= 20 - 2 r \geq 3 r

= 20 \geq 5 r

= r \leq 4

T_{5}

is the greatest term

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Question Text	The numerically greatest term in the expansion of $(3 - 2 x)^{9}$ when $x = 1$ is
Answer Type	Text solution:1
Upvotes	150