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Find the value underset(n rarr oo)("li...

Find the value
`underset(n rarr oo)("lim") underset(k =2)overset(n)sum cos^(-1) ((1 + sqrt((k -1) k(k + 1) (k + 2)))/(k(k + 1)))`

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To solve the limit \[ \lim_{n \to \infty} \sum_{k=2}^{n} \cos^{-1} \left( \frac{1 + \sqrt{(k-1)k(k+1)(k+2)}}{k(k+1)} \right), \] we will break down the problem into manageable steps. ...
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