Question

Calculați:$x=\frac{1}{1*5} + \frac{1}{9*5} + \frac{1}{9*13} +.......+ \frac{1}{81*85}$
!!DAU COROANA!!

Answer 1

Răspuns:

Explicație pas cu pas:

1 -1/5 = 4/1*5,  1/1*5 = 1/4(1 -1/5)

1/5 -1/9 = 4/5*9,  1/9*5 = 1/4(1/5 -1/9)

1/9 -1/13 = 4/9*13,  1/9*13 = 1/4(1/9 -1/13)

....

1/81*85 = 4/81*85,  1/81*85 = 1/4(1/81 - 1/85)

x = 1/4(1 -1/5 +1/5 -1/9 +1/9 -1/13 +...+1/81 -1/85) =

1/4(1 - 1/85) = 1/4 *84/85 = 21/85