Question

1/20 + 1/30 + 1/42 + 1/56 ....+1/306

Answer 1

Răspuns:

1/20 + 1/30 + 1/42 + ... + 1/306 =

1/4*5 + 1/5*6 + 1/6*7 + ... + 1/17*18 =

(exprim pe 1 ca 5-4 la prima fractie, 1 ca 6-5 la a doua etc)

5-4/4*5 + 6-5/5*6 + 7-6/6*7 + ...+18-17/17*18 =

(desfac fiecare fractie ca o diferenta de doua fractii)

5/4*5 - 4/4*5 + 6/5*6 - 5/5*6 + 7/6*7 - 6/6*7 + ... + 18/17*18 - 17/17*18 =

(fac simplificari)

1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/17 - 1/18 =

(reduc fractiile )

1/4 - 1/18 =

9/36 - 2/36 =

7/36