First slide

Binomial theorem for negative integral and rational Index

Question

$The range of x for which the expansion of (4 + 5 x)^{- 7 / 3} is valid$

Very Easy

A

$(\frac{3}{5}, \frac{4}{5})$
B

$(- \frac{4}{5}, \frac{4}{5})$
C

$(- \frac{4}{5}, - \frac{2}{5})$
D

none

Solution

$The expansion is valid \Rightarrow |\frac{5 x}{4}| < 1 \Rightarrow | x | < \frac{4}{5} \Rightarrow - \frac{4}{5} < x < \frac{4}{5} .$

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