Question

Să se calculeze suma

1+3 la puterea -1 + 3 la puterea -2 + 3 la puterea -3.

Explicit vă rog.

Bănuiesc că se face cu ajutorul progresiilor geometrice, am încercat, dar nu înțeleg.

Answer 1

 

$\displaystyle\bf\\ 1+3^{-1}+3^{-2}+3^{-3}=\\\\=1+\frac{1}{3^1}+\frac{1}{3^2}+\frac{1}{3^3}=\\\\\\=\frac{1}{1} +\frac{1}{3}+\frac{1}{9}+\frac{1}{27}=~~~~(\text{Numitorul comun = 27})\\\\\\=\frac{27}{27} +\frac{9}{27}+\frac{3}{27}+\frac{1}{27}=\\\\\\=\frac{27+9+3+1}{27}=\\\\\\=\frac{27+3+9+1}{27}=\\\\\\=\frac{30+10}{27}=\\\\\\=\boxed{\bf\frac{40}{27}}$