\[
\begin{array}{l}
15)Let\;a_{n + 1} \;be\left\{ \begin{array}{l}
a_n + \frac{1}{n},a_n^2 < 2 \\
a_n - \frac{1}{n},a_n^2 > 2 \\
\end{array} \right.and\;also\;given\;a_1 = 1 \\
Show\;that\left| {a_n - \sqrt 2 } \right| < \frac{1}{n},\forall n \in N,n>2 \\
\end{array}
\]
__________________
$$\int_{0}^{\frac{\pi}{2}}\frac{a\cos x-b\sin x}{a\sin x+b\cos x}dx=\ln\left(\frac{a}{b}\right)$$
BUT $$\int_{0}^{\frac{\pi}{2}}\frac{a\cos x+b\sin x}{a\sin x+b\cos x}dx=\frac{\pi ab}{a^{2}+b^{2}}+\frac{a^{2}-b^{2}}{a^{2}+b^{2}}\ln\left(\frac{a}{b}\right)$$
14 ธันวาคม 2006 23:09 : ข้อความนี้ถูกแก้ไขแล้ว 2 ครั้ง, ครั้งล่าสุดโดยคุณ Timestopper_STG
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