- #1
karush
Gold Member
MHB
- 3,269
- 5
$\tiny{242.10.3.27}$
evaluate
$$S_j=\sum_{j=1}^{\infty}3^{-3j}=$$
rewrite
$$S_j=\sum_{j=1}^{\infty} 27^{j-1}$$
using the geometric formula
$$\sum_{n=1}^{\infty}ar^{n-1}=\frac{a}{1-r}, \left| r \right|<1$$
how do we get $a$ and $r$ to get the answer of $\frac{1}{26}$
![Hot beverage :coffee: ☕](https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/2615.png)
evaluate
$$S_j=\sum_{j=1}^{\infty}3^{-3j}=$$
rewrite
$$S_j=\sum_{j=1}^{\infty} 27^{j-1}$$
using the geometric formula
$$\sum_{n=1}^{\infty}ar^{n-1}=\frac{a}{1-r}, \left| r \right|<1$$
how do we get $a$ and $r$ to get the answer of $\frac{1}{26}$
![Hot beverage :coffee: ☕](https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/2615.png)