Question

23. a) Calculati
b) Folosind rezultatul de la punct a), calculati
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Answer 1

Răspuns:

Explicație pas cu pas:

a)

$\frac{1}{2^{n-1}} -\frac{1}{2^{n}} = \frac{1}{2^{n-1}} - \frac{1}{2*2^{n-1}}=\frac{1}{2^{n-1}} (1-\frac{1}{2} )=\frac{1}{2^{n-1}}*\frac{1}{2} =\frac{1}{2^n}$

b)

$\frac{1}{2} -(\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{10}})=\frac{1}{2} -\frac{1}{2^2}-\frac{1}{2^3}-\frac{1}{2^4}-...-\frac{1}{2^{10}}=\frac{1}{2^2}-\frac{1}{2^3}-\frac{1}{2^4}-...-\frac{1}{2^{10}}=\frac{1}{2^3}-\frac{1}{2^4}-...-\frac{1}{2^{10}}= ... =\frac{1}{2^{9}}-\frac{1}{2^{10}} = \frac{1}{2^{10}}$