find-the-following-please-S-k-1-n-1-k-k-1-k-2-

Question Number 154896 by maged last updated on 22/Sep/21

f i n d t h e f o l l o w i n g ? p l e a s e

S = \underset{k = 1}{\sum^{n}} \frac{1}{k (k + 1) (k + 2)}

Commented by benhamimed last updated on 23/Sep/21

Σ \frac{1}{k (k + 1) (k + 2)} = Σ \frac{1}{2} (\frac{1}{k} - \frac{2}{k + 1} + \frac{1}{k + 2})

= \frac{1}{2} (1 - \frac{2}{2} + \frac{1}{3} + \frac{1}{2} - \frac{2}{3} + \frac{1}{4} + \frac{1}{3} - \frac{2}{4} + \frac{1}{5} + \dots

\frac{1}{n - 1} - \frac{2}{n} + \frac{1}{n + 1} + \frac{1}{n} - \frac{2}{n + 1} + \frac{1}{n + 2})

= \frac{1}{2} (\frac{1}{2} - \frac{1}{n + 1} + \frac{1}{n + 2})

Commented by maged last updated on 23/Sep/21

T h a n k y o u

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