Matematică
Cotovanu14
2015-11-14 19:34:54
Ex se afla in imagine....... .
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mariusbirta28
2015-11-14 19:49:45

[latex]S_5=frac{1}{4}(frac{1}{1cdot2}+frac{1}{2cdot 3}+...frac{1}{1007cdot 1008})=\ frac{1}{4}(frac{2-1}{1cdot2}+frac{3-2}{2cdot3}+frac{4-3}{3cdot4}+...frac{1008-1007}{1007cdot1008})=\ frac{1}{4}(frac{2}{1cdot2}-frac{1}{2}+frac{3}{2cdot3}-frac{2}{2cdot3}+frac{4}{3cdot4}-frac{3}{3cdot4}+...frac{1008}{1007cdot1008}-frac{1007}{1007cdot1008})=\ [/latex] [latex]frac{1}{4}(1-frac{1}{2}+frac{1}{2}-frac{1}{3}+frac{1}{3}-frac{1}{4}+....+frac{1}{1007}-\frac{1}{1008})=frac{1}{4}(1-frac{1}{1008})=[/latex] [latex]frac{1}{4}cdotfrac{1007}{1008}=frac{1007}{4032}[/latex]

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