# If $x$ is positive, the first negative term in the expansion of $\dpi{100} (1+x)^{27/5}$ is Option 1) 5th term Option 2) 8th term Option 3) 6th term Option 4) 7th term

Answers (1)

As we learnt in

Binomial Theorem for Rational index -

$\left ( 1+x \right )^{n}= 1+nx+\frac{n\left ( n-1 \right )x^{2}}{2!}+\frac{n\left ( n-1 \right )\left ( n-2 \right )x^{3}}{3!}+-----$

- wherein

use $\dpi{120} ^{n}c_{r}= \frac{n!}{r!(n-r)!}$

$\dpi{120} n> 0$

$(1+x)^{\frac{27}{5}}$

If $n={\frac{27}{5}}$

n - 6 < 0

We will get the factor of n - 6 in the seventh term.

Correct option is 4.

Option 1)

5th term

This is an incorrect option.

Option 2)

8th term

This is an incorrect option.

Option 3)

6th term

This is an incorrect option.

Option 4)

7th term

This is the correct option.

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