Question

Write $\frac 15+\left(\frac 15\right)^2+\left(\frac 15\right)^3+\left(\frac 15\right)^4$ as a decimal

Answer 1

Answer: .2496

Aops Question

Explanation:

This problem becomes easier if we write $\dfrac{1}{5}$ as $\dfrac{2}{10}$, so that all the denominators in our sum are powers of 10. Then

\begin{align*}

\frac15 + \left(\frac15\right)^2 + \left(\frac15\right)^3 + \left(\frac15\right)^4

&= \frac2{10} + \left(\frac2{10}\right)^2 + \left(\frac2{10}\right)^3 + \left(\frac2{10}\right)^4 \\

&= \frac2{10} + \frac4{100} + \frac8{1000} + \frac{16}{10{,}000} \\

&= 0.2 + 0.04 + 0.008 + 0.0016 \\

&= \boxed{0.2496}.

\end{align*}

Answer 2

0.2496

Explanation:

what you could do is make the all the 1/5 into 2/10's.

then you could multiply all of them (2/10) squared (2/10) cubed and (2/10)^4

now you would have 2/10 4/100 8/1000 16/10000

now you can change it into decimals and add

0.2 +0.04+0.008+0.0016

now all you have to do is add when you do you get 0.2496

there are many ways you could do this problem but this is the most efficient becuause I used another way but it was not helpfull.