I'm trying to prove that:
(1+x)^-5/2 < 1
Sorry I know it's really easy but I'm just not seeing what to do!
Thanks in advance!
Hello, hunkydory19!
As given, the statement is not true . . .
It is necessary that $\displaystyle x > 0.$Prove: .$\displaystyle (1+x)^{-5/2} \:<\:1$
Then we have: .$\displaystyle 1 + x \:>\:1$
Raise both sides to the power $\displaystyle \frac{5}{2}\!:\;\;(1 + x)^{\frac{5}{2}} \:>\:1$
Take reciprocals: .$\displaystyle \frac{1}{(1+x)^{\frac{5}{2}}} \:<\:1\quad\Rightarrow\quad(1+x)^{-\frac{5}{2}} \:<\:1$