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\text { If }(r+1)^{\text {th }} term is the first negative term in the expansion of (1+x)^{9 / 2}, x>0 than the value of r is 

Option: 1

7


Option: 2

5


Option: 3

2


Option: 4

6


Answers (1)

best_answer

We have,

T_{r+1}=\frac{\frac{9}{2}\left(\frac{9}{2}-1\right)\left(\frac{9}{2}-2\right) \ldots\left(\frac{9}{2}-r+1\right) x^r}{r !}

This will be the first negative term when

\frac{9}{2}-r+1<0 \text {, i.e., } r>\frac{11}{2}

Hence, r = 6.

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Shailly goel

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