Tìm n biết \(\frac{4}{{3.5}} + \frac{8}{{5.9}} + \frac{{12}}{{9.15}} + \ldots + \frac{{32}}{{n(n + 16)}} = \frac{{16}}{{25}}\)
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Lời giải:
Báo sai\(\begin{array}{l} \frac{4}{{3.5}} + \frac{8}{{5.9}} + \frac{{12}}{{9.15}} + \ldots + \frac{{32}}{{n(n + 16)}} = \frac{{16}}{{25}}\\ \Rightarrow 2\left( {\frac{2}{{3.4}} + \frac{4}{{5.9}} + \frac{6}{{9.15}} + \ldots + \frac{{16}}{{n(n + 16)}}} \right) = \frac{{16}}{{25}}\\ \Rightarrow 2\left( {\frac{1}{3} - \frac{1}{{n + 16}}} \right) = \frac{{16}}{{25}} \Leftrightarrow \frac{1}{3} - \frac{1}{{n + 16}} = \frac{8}{{25}}\\ \Rightarrow \frac{1}{{n + 16}} = \frac{1}{3} - \frac{8}{{25}} = \frac{1}{{75}}\\ \Rightarrow n + 16 = 75\\ \Rightarrow n = 75 - 16 = 59 \end{array}\)
