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设数列{an}满足:当n=2k-1(k∈N*)时,an=n;当n=2k(k∈N*)时,an...
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设数列{a
n}满足:当n=2k-1(k∈N
*)时,a
n=n;当n=2k(k∈N
*)时,a
n=a
k.
(1)求a
2+a
4+a
6+a
8+a
10+a
12+a
14+a
16;
(2)若
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANQAAAAgCAYAAABq3VYXAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAA95JREFU
eF7tWwt2rSAM5G3Z7bgT1+Eq3ISPjyioV0IgoUo87WlPLxBmyJhA6L9VP0oeYUAYqMOAEZQ8woAw
UIcBVWcYGUUYEAZstnfQsKzToEz6Z7+HadEfzetkf8ojDAgDEAY2QTkxORG5Z5kGLaxhfaWe5nEd
Zwj8wjZfssOFpZDyZPfGODZBzet4I555HHWMgj0+skF/wkZFtuIi9Ut2uLAglxTcrTGOKEKpYVpb
J3jz6NNOLWZNjsKEGgCpX7HjX2Chw0H/FjkpF2dgZSAbNsZxs4dqleZte7hdQCZqKnDqdgjk2Ace
0TKMtN+yAxXPXTsuzpDSAHf7Szgup3x+crmBAZrq3S2sYc7ajYwax0eK++Et9TU7YK9LNeTiLDWP
0s8b41Daky9RwB1IwPdPpRzoE5B1ONszf8OmoL9I/ZqdYuKDAbg4qznnu7Ea41BGPJdoZPYujIIy
cwhPGPUZ4+XUMWsdfpD6NTtZnKQac3GWmkfp541xKJfiPe0xShGm+8dpmNs7uSP7ZdVf8WOjTCIV
/EEq2I59oWx7safct7GdNLMZLUqxZJgibdoYhxqtw3gnBjgRBRtWJMHp3j6fk3B2R0furSB2TBsv
oq19HD0BBEDsGIzIAxjADOo1AWGpZ45sJCYcL7x6dF8zq7UQyzxHpQO7n8Tu5Z4mZaJvtIWBn2jW
wirj1GcAKCgfwbbUcIsU2W/uKvOnFdRligYrhaACQ1a0uceqVbjkGmTzH8tj+DuX/Vp20jiAgjIT
0oMZQnyxFVt0LcbGK6jrQUYxgFBKx/3JLwvKRGPtL8Ok74YO+qV8d9pak1aqsQA44IKyhEx73m82
+N+PUNtLhGqB/LjYvRr1vCqOb/1Fi8nduUbegKk4H+xQKRxgQcWngQVFVyySvR9fhMq5y1gK69tp
n1uzcXa7RuNL7wzIaRxAQZ2cuKToWup5NgdHnvJl2L6tz2X0z2764rf2ppLfpYYQW0m6BymZZBN/
6vBUMgHggAnqJCDafUWKEQZB2fQ2OIMDXLhMzfr585YRv2zmtnei1BBFJO+wuSGqtGQCgVkBB0hQ
ZwH5+37se6iolkCTNrhrV+cLtvWvYcV26CMuxJ+wbdhKDcTZSQ0cIEFhiZZ+nTJAVmpgyE7CJUPg
EEF16vOUsOm2BLyCwuAQQVF6Vpdj55UaHv+X6Xprm+VAyi1bHg6/1CKoLp2eDjRtqYEvQmFxiKDo
fKu7kelLDTyCKsEhgurO7YkAs5QaGARViEMEReRfPQ3LUmp4SclEBNWT5wtWcgZEUOQUi4GeGBBB
9bTagpWcAREUOcVioCcG/gNhQZQWHsKddwAAAABJRU5ErkJggg==
)
,证明:S
n=4
n-1+S
n-1(n≥2);
(3)证明:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIcAAAAqCAYAAACZZUg6AAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
.
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