计算(x+1/x)(x2+1/x2)(x4+1/x4)…(x16+1/x16)(x2-1)
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计算(x+1/x)(x2+1/x2)(x4+1/x4)…(x16+1/x16)(x2-1)
数字代表几次幂,1/x2读作x的二次幂分之一,
数字代表几次幂,1/x2读作x的二次幂分之一,
![计算(x+1/x)(x2+1/x2)(x4+1/x4)…(x16+1/x16)(x2-1)](/uploads/image/z/19893773-29-3.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%88x%2B1%2Fx%29%28x2%2B1%2Fx2%29%28x4%2B1%2Fx4%29%E2%80%A6%EF%BC%88x16%2B1%2Fx16%29%28x2-1%29)
原式=(x+1/x)(x-1/x)(x^2+1/x^2)……(x^16+1/x^16)(x^2-1)/(x-1/x)
=(x^2-1/x^2)(x^2+1/x^2)(x^4+1/x^4)……(x^16+1/x^16)(x^2-1)/(x-1/x)
=……
=(x^16-1/x^16)(x^16+1/x^16)(x^2-1)/(x-1/x)
=(x^32-1/x^32)(x^2-1)/(x-1/x)
=(x^32-1/x^32)(x^2-1)/[(x^2-1)/x]
=x(x^32-1/x^32)
=x^33-1/x^31
x^33表示x的33次幂
=(x^2-1/x^2)(x^2+1/x^2)(x^4+1/x^4)……(x^16+1/x^16)(x^2-1)/(x-1/x)
=……
=(x^16-1/x^16)(x^16+1/x^16)(x^2-1)/(x-1/x)
=(x^32-1/x^32)(x^2-1)/(x-1/x)
=(x^32-1/x^32)(x^2-1)/[(x^2-1)/x]
=x(x^32-1/x^32)
=x^33-1/x^31
x^33表示x的33次幂
4/5x4+2/5x2+1/5x16
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