Question

6) Calculati a + b , daca a) a=1/2+/1/3+1/4+...+1/50 b=1/2+2/3+3/4+...+49/50 b)a= 1/1+1/3+1/5+1/7... +1/79 si b=2/3+4/5+6/7+...+78/79 c)a= 8/9+9/10+10/11+...+86/87 si b= 1/9+1/10+1/11+...+1/87

Answer 1

Răspuns:

Explicație pas cu pas:

b)

a= 1/1+1/3+1/5+1/7... +1/79 si

      b=2/3+4/5+6/7+...+78/79

a+b = 1 + 3/3 + 5/5 + 7/7 + ... + 79/79 =

          1 + 1 + 1 + 1 + ... + 1 = (dupa primul 1 avem inca 79-3 / 2  + 1 = 76/2 + 1 = 38 + 1 = 39 de 1)

          1 + 39 = 40.

c) a= 8/9+9/10+10/11+...+86/87 si

   b= 1/9+1/10+1/11+...+1/87

a+b = 9/9 + 10/10 + 11/11 + ... + 87/87 =

           1+1+1+...+1(de 87-9+1= 79 de ori) =

          79.