数列an满足a1=2012,a n+1 +a n +n²=0 求a11这怎么做啊?求解,急谢了
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![数列an满足a1=2012,a n+1 +a n +n²=0 求a11这怎么做啊?求解,急谢了](/uploads/image/z/13309564-4-4.jpg?t=%E6%95%B0%E5%88%97%EF%BD%81n%E6%BB%A1%E8%B6%B3a1%3D2012%2Ca+n%2B1+%2Ba+n+%2Bn%26%23178%3B%3D0+%E6%B1%82a11%E8%BF%99%E6%80%8E%E4%B9%88%E5%81%9A%E5%95%8A%3F%E6%B1%82%E8%A7%A3%2C%E6%80%A5%E8%B0%A2%E4%BA%86)
数列an满足a1=2012,a n+1 +a n +n²=0 求a11这怎么做啊?求解,急谢了
数列an满足a1=2012,a n+1 +a n +n²=0 求a11
这怎么做啊?求解,急谢了
数列an满足a1=2012,a n+1 +a n +n²=0 求a11这怎么做啊?求解,急谢了
a(n+1)+an +n²=0,则
a(n+2)+a(n+1)+(n+1)²=0
减去上式得
a(n+2)=an+n²-(n+1)²=an-2n-1
于是
a11=a9-2*9-1
=a7-2*7-1-2*9-1
=a5-2*5-1-2*7-1-2*9-1
=a3-2*3-1-2*5-1-2*7-1-2*9-1
=a1-2*1-1-2*3-1-2*5-1-2*7-1-2*9-1
=2012-2(1+3+5+7+9)-5
=1957
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