Question

14). Calculați suma:​

Answer 1

Răspuns:

$\boxed{a) \frac{364}{729} }$

$\boxed{ b)\frac{63}{64} }$

Explicație pas cu pas:

$\mathbf{a) \frac{1}{3} + \frac{1}{3 {}^{2} } + \frac{1}{ {3}^{3} } + \frac{1}{3 { }^{4} } + \frac{1}{ {3}^{5} } + \frac{1}{ {3}^{6} } }$

$\mathbf{ \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81} + \frac{1}{243} + \frac{1}{729} }$

$\mathbf{ \frac{27 + 9 + 3 + 1}{81} + \frac{1}{243} + \frac{1}{729} }$

$\mathbf{ \frac{40}{81} + \frac{1}{243} + \frac{1}{729} }$

$\mathbf{ \frac{121}{243} + \frac{1}{729} = \frac{364}{729} }$

$\mathbf{b) \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16 } + \frac{1}{32} + \frac{1}{64} }$

$\mathbf{ \frac{1 \times 32}{2 \times 32} + \frac{1 \times 16}{4 \times 16} + \frac{1 \times 8}{8 \times 8} + \frac{1 \times 4}{16 \times 4} + \frac{1 \times 2}{32 \times 2} + \frac{1}{64} }$

$\mathbf{ \frac{32}{64} + \frac{16}{64} + \frac{8}{64} + \frac{4}{64} + \frac{2}{64} + \frac{1}{64} }$

$\mathbf{ \frac{32 + 16 + 8 + 4 + 2 + 1}{64} = \frac{63}{64} }$

Bafta!