Font (2 3) - + Letter spacing (4 5) - + Word spacing (6 7) - + Line spacing (8 9) - +

Question 2

2. (i) Show that

{{1}\over{1\cdot 3}}+{{1}\over{2\cdot 4}}+\dots+{{1}\over{N\cdot(N+2)}}={{1}% \over{2}}\Bigl(1+{{1}\over{2}}-{{1}\over{N+1}}-{{1}\over{N+2}}\Bigr),

where $a\cdot b$ denotes the product of $a$ and $b$ .

(ii) Deduce the value of the sum of the series

{{1}\over{1\cdot 3}}+{{1}\over{2\cdot 4}}+\dots.

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