Question

ofer 15 puncte va rog exercitiul 44

Answer 1

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

b).$\frac{1}{2} - \frac{1}{2^2}-...- \frac{1}{2^10}$=$\frac{1}{2^2}- \frac{1}{2^3}-... \frac{1}{2^{10}}$=$\frac{1}{2^{10}}$
Explicatie: am aplicat formula de la punctul a pentru primii doi termeni si tot asa pana am ajuns la ultimul