Răspuns:
Explicație pas cu pas:
a)
[tex]\frac{1}{2^{n-1}} -\frac{1}{2^{n}} = \frac{1}{2^{n-1}} - \frac{1}{2*2^{n-1}}=\frac{1}{2^{n-1}} (1-\frac{1}{2} )=\frac{1}{2^{n-1}}*\frac{1}{2} =\frac{1}{2^n} \\[/tex]
b)
[tex]\frac{1}{2} -(\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{10}})=\frac{1}{2} -\frac{1}{2^2}-\frac{1}{2^3}-\frac{1}{2^4}-...-\frac{1}{2^{10}}=\frac{1}{2^2}-\frac{1}{2^3}-\frac{1}{2^4}-...-\frac{1}{2^{10}}=\frac{1}{2^3}-\frac{1}{2^4}-...-\frac{1}{2^{10}}= ... =\frac{1}{2^{9}}-\frac{1}{2^{10}} = \frac{1}{2^{10}}[/tex]
