f(x)=x^3-3x^2,求f(1⼀2013)+f(2⼀2013)+f(3⼀2013)+.+f(4024⼀2013)+f(4025⼀2013

2025-06-29 10:20:14
推荐回答(1个)
回答1:

f(x)+f(2-x)=x³-3x²+(2-x)³-3(2-x)²
=x³-3x²+8-12x+6x²-x³-12+12x-3x²
=-4
所以
f(1/2013)+f(2/2013)+f(3/2013)+....+f(4024/2013)+f(4025/2013)
=[f(1/2013)+f(4025/2013)]+[f(2/2013)+f(4024/2013)]
+...+[f(2012/2013)+f(2014/2013)]+f(2013/2013)
=2012×(-4)+f(1)
=-8050