英语数学综合题

题目

英语数学综合题
1.The fraction 2/(x^2-3x+2)can be written as an infinite series.Find the sum of the first four terms of the series espansion for x=-1 and x=-2.
2.Many different seven digit integers can be formed by permuting the digits 1-7;like 1234567 and 7653412.What is the sum of all seven digit numbers.
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答案

1.2/(x^2-3x+2)=2/(1-x)-1/(1-x/2)=2(1+x+x^2+x^3+x^4+...)-(1+x/2+x^2/4+x^3/8+x^4/16+...)=1+3x/2+7x^2/4+15x^3/8+31x^4/16+...当x=-1,-2是,用展开式的前四项求和：S(-1)=1-3/2+7/4-15/8=-5/8S(-2)=1-3+7-15=-102....