x,-2X^2,4X^3,-8X^4.n 根据你发现的规律写出第n个式子是什么?

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x,-2X^2,4X^3,-8X^4.n 根据你发现的规律写出第n个式子是什么?

x,-2X^2,4X^3,-8X^4.n 根据你发现的规律写出第n个式子是什么?
x,-2X^2,4X^3,-8X^4.n 根据你发现的规律写出第n个式子是什么?

x,-2X^2,4X^3,-8X^4.n 根据你发现的规律写出第n个式子是什么?
首先观察带X项的系数,分别是:
1 -2 4 -8 .
1=2^0 ,-2=(-1)*(2^1),4=2^2 ,-8=(-1)*(2^3)
奇数项正,偶数项负,且第n项系数的绝对值是 2^(n-1) ,
那么第n项的系数就是 [(-1)^(n+1)]*[2^(n-1)] ;
而带 X 的部分依次是:
X X^2 X^3 X^4 .
即第n项带X的部分是 X^n
所以第n个式子是:[(-1)^(n+1)]*[2^(n-1)] X^n
满意请采纳,谢谢~

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