Question

Aratati ca numarul rational
$a = \frac{1}{5 \times 6} + \frac{1}{6 \times 7} + ... + \frac{1}{70 \times 71} + \frac{1}{71}$
este mai mic decat 1.
​

Answer 1

Răspuns:

Explicație pas cu pas:

ak=1/k×(k+1)=1/k-1/(k+1)

1/5×6=1/5-1/6

1/6×7=1/6-1/7

.....................

1/70×71=1/70-1/71

        1/71=1/171

..............................

      a=1/5    ⇒a<1