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Homework Statement
Find the Sum of [tex]\sum\limits_{n = 2}^\infty {\frac{1}{{n\left( {n - 1} \right)}}} [/tex]
Homework Equations
[tex]\sum\limits_{n = 1}^\infty {\frac{1}{{n\left( {n + 1} \right)}} = 1} [/tex]
The Attempt at a Solution
[tex]\sum\limits_{n = 2}^\infty {\frac{1}{{n\left( {n + 1} \right)}} = \sum\limits_{n = 1}^\infty {\frac{1}{{n\left( {n + 1} \right)}} - a_1 = 1} - a_1 = 1 - \frac{1}{{1\left( {1 + 1} \right)}} = 1 - \frac{1}{2} = \frac{1}{2}}
[/tex]
But the book says the answer is 1. I can see it being 1 if n=1 in the sumation symbol, but it is n=2, so don't I have to subtract the value of a1 from the sum computed from the formula?