论坛 › 难题征解 › 数列通项问题，此题条件充分吗

manthanein 发表于 2015-11-22 22:18:54

\(a_{1}=0\)
\(a_{2}=-a_{5}\)
\(a_{3}=a_{3}\)
\(a_{4}=0\)
\(a_{5}=a_{5}\)
\(a_{6}=2a_{3}\)
\(a_{7}=a_{3}\)
\(a_{8}=a_{3}\)
\(a_{9}=a_{5}-a_{3}\)
\(a_{10}=a_{10}\)
\(a_{11}=a_{3}\)
\(a_{12}=2a_{3}-a_{10}\)
\(a_{13}=a_{20}+a_{3}-a_{10}\)
\(a_{14}=a_{3}+a_{20}\)
\(a_{15}=-a_{3}\)
\(a_{16}=a_{10}+a_{5}-2a_{3}\)
\(a_{17}=-a_{10}\)

manthanein 发表于 2015-11-22 22:22:53

同时\(a_{10}=a_{5}+a_{14}\)
所以\(a_{10}=a_{3}+a_{5}+a_{20}\)
所以\(a_{20}=a_{10}-a_{3}-a_{5}\)

manthanein 发表于 2015-11-22 22:24:47

\(a_{13}=-a_{5}\)
\(a_{14}=a_{10}-a_{5}\)

manthanein 发表于 2015-11-22 22:30:33

本帖最后由 manthanein 于 2015-11-22 22:37 编辑

而\(a_{12}=a_{7}+a_{19}\)
\(a_{19}=a_{3}-a_{10}\)

\(a_{18}=a_{18}\)
\(a_{19}=a_{3}-a_{10}\)
\(a_{20}=a_{10}-a_{3}-a_{5}\)
\(a_{21}=a_{21}\)
\(a_{22}=a_{22}\)

manthanein 发表于 2015-11-22 22:39:24

\(a_{16}=a_{8}+a_{23}\)
\(a_{23}=a_{10}+a_{5}-3a_{3}\)

manthanein 发表于 2015-11-22 22:42:17

\(a_{15}=a_{9}+a_{23}\)
所以\(a_{23}=-a_{5}\)
所以\(-a_{5}=a_{10}+a_{5}-3a_{3}\)
所以\(a_{10}=3a_{3}-2a_{5}\)

manthanein 发表于 2015-11-22 22:46:33

\(a_{1}=0\)
\(a_{2}=-a_{5}\)
\(a_{3}=a_{3}\)
\(a_{4}=0\)
\(a_{5}=a_{5}\)
\(a_{6}=2a_{3}\)
\(a_{7}=a_{3}\)
\(a_{8}=a_{3}\)
\(a_{9}=a_{5}-a_{3}\)
\(a_{10}=3a_{3}-2a_{5}\)
\(a_{11}=a_{3}\)
\(a_{12}=2a_{5}-a_{3}\)
\(a_{13}=-a_{5}\)
\(a_{14}=3a_{3}-3a_{5}\)
\(a_{15}=-a_{3}\)
\(a_{16}=a_{3}-a_{5}\)
\(a_{17}=2a_{5}-3a_{3}\)
\(a_{18}=a_{18}\)
\(a_{19}=2a_{5}-2a_{3}\)
\(a_{20}=2a_{3}-3a_{5}\)
\(a_{21}=a_{21}\)
\(a_{22}=a_{22}\)

manthanein 发表于 2015-11-22 22:56:40

\(a_{24}=a_{16}+a_{13}-a_{13}\)
所以\(a_{24}=a_{3}-a_{5}\)

manthanein 发表于 2015-11-22 22:58:36

\(a_{18}=a_{9}+a_{26}\)
\(a_{26}=a_{18}+a_{3}-a_{5}\)

manthanein 发表于 2015-11-22 23:03:39

\(a_{22}=a_{11}+a_{32}\)
\(a_{32}=a_{22}+a_{17}-a_{15}\)
所以\(a_{11}+a_{17}=a_{15}\)
所以\(2a_{5}-2a_{3}=-a_{3}\)
所以\(2a_{5}=a_{3}\)

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