Question

rezolvati exercitiul din imagine.​

Answer 1

Răspuns:

Explicație pas cu pas:

4/5 + 4/5^2 + 4/5^3 + 4/5^4 + 4/5^5 + 4/5^6

= 4*(1/5 + 1/5^2 + 1/5^3 + 1/5^4 + 1/5^5 + 1/5^6)

____________

1/5 + 1/5^2 + 1/5^3 + 1/5^4 + 1/5^5 + 1/5^6

= 5^5/5^6 + 5^4/5^6 + 5^3/5^6 + 5^2/5^6 + 5/5^6 + 1/5^6

= (5^5 + 5^4 + 5^3 + 5^2 + 5 + 1)/5^6

S = 5^5 + 5^4 + 5^3 + 5^2 + 5 + 1

5S = 5^6 + 5^5 + 5^4 + 5^3 + 5^2 + 5

5S - S = 5^6 + 5^5 + 5^4 + 5^3 + 5^2 + 5 - 5^5 - 5^4 - 5^3 - 5^2 - 5 - 1

4S = 5^6 - 1

S = (5^6 - 1)/4

1/5 + 1/5^2 + 1/5^3 + 1/5^4 + 1/5^5 + 1/5^6 = (5^6 - 1)/4*5^6

____________

4/5 + 4/5^2 + 4/5^3 + 4/5^4 + 4/5^5 + 4/5^6

= 4*(1/5 + 1/5^2 + 1/5^3 + 1/5^4 + 1/5^5 + 1/5^6) = 4*(5^6 - 1)/4*5^6

= (5^6 - 1)/5^6