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已知数列{an}的前n项和Sn是二项式(1+2x)2n(n∈N*)展开式中含x奇次幂的系数...
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已知数列{a
n}的前n项和S
n是二项式(1+2x)
2n(n∈N
*)展开式中含x奇次幂的系数和.
(1)求数列{a
n}的通项公式;
(2)设f(n)=
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACsAAAAqCAYAAAAqAaJlAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
,求c
n=f(0)+f(
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAjCAYAAACgj+sEAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAK5JREFU
OE/tVNsNBCEI9FqmHTqhDquwCc6R9XIGNrtmX8nlSIw/zuDAwEtrpJkAYCbSzOP2GwcoopRIpcRU
IyAz9NSzF9BIs/IfMJY3aNxMlVrT0Ac7nH3zTrDGhrluyNAF7rljez+v4fiIXqABZvv2TlGhTS8B
xHWa8dgWQBFSClaHWQMuJVHhvi0sy6pbwTbYeSGIVlPN4NnWvmPWcGxdR1aJNDi2z9ShCL85cW/e
wOv/veReewAAAABJRU5ErkJggg==
)
)+f(
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAjCAYAAACgj+sEAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAOxJREFU
OE/NVMENBCEI9Fq2HTuhDqqwCc6RVQ/Fy5pLNmfiYzcMzODAS8oJJweAkxNOgisbA+AEenojSXay
DUAmiYmvEJYEUP8eyA7IzCZjpuhW2WsAvW8VZrqcgjjxk+iGMnpsKodSFopJmvy58gLgFIW8fl5I
A0BnDO8ifNbRARDZH609Xlip/WiNG8Z6oMIq1BOv/1Z7/4eGGyxMyANtlWLkOr/lqtFg789vdx4A
gtEQrPaGc6Pjc9WACStrhfosaJXtiNYN0SmNBJu9tGbb0VFrXHRGtqaDhTwNSzYkqF3zF8EjD3fm
pmNKb26f41Jh+xBoAAAAAElFTkSuQmCC
)
)+…+f(
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAjCAYAAACgj+sEAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAJ1JREFU
OE/tVMENgCAMxJW7Dpt0DqZgidOjKCqY2I/hYRMSSNrr9dqyYLPgMQZ4LHicC5spAxJiCFQKMZFg
hsr5fSVda2BQRCrOAs1bmAqEl5tZQFaIKDSa857FMg4yEK1RagA9fpHVOJ/RnuhYHyqdhrbXkaCj
Gjo0AhTVKMJDDZ5uzzga1P/tmXe8PV34aEX/jasfAD+Df+OOCV0Be6risgQmti4AAAAASUVORK5C
YII=
)
),求
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAqCAYAAABGB/BgAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAASpJREFU
WEftV0ESwyAItF/2O/6Ed/gKP0GBaqrJNEISesjEmbSHblxhF6EvpBW8F5N4r+BNIJlSkxTAGCJC
Ub+xAHUkObFu9HiSyJkypodEL+OTLkuduLtLCpHr5POkrFfSVvG2fQe0ruJPENwskiam1/fN0nXS
OKrXHwur0tRAf07XMiwoL0ADXiIpEDFEQJl26OU4mXuseCLhtproU7useGpafKrZyXt6K16ulZyU
GlQmK15IJL+t1XEHbNp0m/aR/sYXhNi655j+qkn9cUUgG1K7HdPJmmzxBdIyJ3O0i5E0A/cRDciu
NBN8o5kW4yGSlWN9SCiS1NWaC0mGWtjVPJeTcHrXc9mlJKN+GaGmbJekWXhr4+0VJLbtpsz+X9k0
Eu2Ntoe7D8kbJj8VVCraYygAAAAASUVORK5CYII=
)
+
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAqCAYAAABGB/BgAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAATZJREFU
WEftV8ERhCAM5FqmnXRCHVRhE7kkBwjeqZtxuIcjM+pn40J2Y+KLZYXZS0lmrzCbwDIFkyyJY4ic
FjiiATGSTKqbXDNJbE+Z6SHBZXzS5amT6e6yQtQ6+VyUcSV9Fe9774DGKv4Cwc1OUsWc9bxZui4a
Bwp/LAylqYL+nK42LIAfQAfeTrKkyCEmtmlHguPJ3OPFC4m2VZI7urx4aVq6q7Od9/RevH1WMoEa
FCYv3kgsv7XVaQes2ohCKdZuuKZzH1+0/TFpFk3KyxqBBlCbe3X3zRim4TdeApiKYYaNwAO39XiH
OTYOBYvR4yhJcxq9ipF0qTg0ejfV9I6FSHIqhQqW0lCsiCYa4J2zrMA7Ex2eZCy8LLkGf7NQ4c22
3dR49pdlKar4zdEhTUApdmH3IXkDs/cNqfhqI+EAAAAASUVORK5CYII=
)
+…+
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAqCAYAAADf/ynVAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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=
)
的值.
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