Problem #2

Value sum the first ten terms of sequence numbers
$latex \frac {1}{1 \cdot 2} + \frac {1}{2 \cdot 3} + \frac {1}{3 \cdot 4} + \frac {1}{4 \cdot 5} + \cdots + \frac {1}{9 \cdot 10} + \frac {1}{10 \cdot 11} = … $

SOLUSI
Perhatikan pola berikut:

$latex \frac {1}{1 \cdot 2} = \frac {1}{2} $

$latex \frac {1}{1 \cdot 2} + \frac {1}{2 \cdot 3} = \frac {2}{3} $

$latex \frac {1}{1 \cdot 2} + \frac {1}{2 \cdot 3} + \frac {1}{3 \cdot 4} = \frac {3}{4} $

$latex \vdots $

Dengan demikian,

$latex \frac {1}{1 \cdot 2} + \frac {1}{2 \cdot 3} + \frac {1}{3 \cdot 4} + \frac {1}{4 \cdot 5} + \cdots + \frac {1}{9 \cdot 10} + \frac {1}{10 \cdot 11} = \frac {..}{..} $

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