Question

Sa se calculeze suma
1+1/5+1/5^2+...+1/5^14​

Answer 1

Răspuns:

Explicație pas cu pas:

S = 1+1/5+1/5^2+...+1/5^14​

S/5 = 1/5+1/5^2+...+1/5^14​ + 1/5^15

S - S/5 = 4S/5 = 1 + 1/5 + 1/5^2 +...+ 1/5^14​ - 1/5 - 1/5^2 -....- 1/5^14​ - 1/5^15

4S/5 = 1 - 1/5^15

4S = 5 - 1/5^14

S = 5/4 - 1/4*5^15