Răspuns :

Semaka2id

Răspuns:

Explicație pas cu pas:

F1=(10ⁿ-2ⁿ*5ⁿ⁻¹)/16*10ⁿ⁻¹=

(10*10ⁿ⁻¹-2*2ⁿ⁻¹*5ⁿ⁻¹)/16*10ⁿ⁻¹=

(10*10ⁿ⁻¹-2*10ⁿ⁻¹)/16*10ⁿ⁻¹=

8*10ⁿ⁻¹/16*10ⁿ⁻¹=1/2

F1=1/2

F2=(6ⁿ⁺¹-3ⁿ)/9(6ⁿ*2-3ⁿ⁻¹)=

(6*6ⁿ-3ⁿ)/9*(6*6ⁿ⁻¹*2-3ⁿ⁻¹)=

(6*2ⁿ*3ⁿ-3ⁿ)/9*(12*2ⁿ⁻¹*3ⁿ⁻¹-3ⁿ⁻¹)=

3ⁿ(6*2ⁿ-1)/9*3ⁿ⁻¹(6*2*2ⁿ⁻¹-1)=

3(6*2ⁿ-1)/9*(6*2ⁿ-1)=1/3

F2=1/3

F=F1-F2=1/2-1/3=

Targoviste44id

[tex]\it F_1=\dfrac{10^n-2^n\cdot5^{n-1}}{16\cdot10^{n-1}} = \dfrac{10^n-10^n\cdot\dfrac{1}{5}}{16\cdot10^n\cdot\dfrac{1}{10}}=\dfrac{10^n(1-\dfrac{1}{5})}{10^n\cdot\dfrac{16}{10}}=\dfrac{4}{5}\cdot\dfrac{10}{16}=\dfrac{1}{2}\\ \\ \\ F_2=\dfrac{6\cdot6^n-3\cdot3^{n-1}}{9(6^n\cdot2-3^{n-1})}=\dfrac{3(2\cdot6^n-3^{n-1})}{9(2\cdot6^n-3^{n-1})}=\dfrac{1}{3}[/tex]