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计算 1⼀x-1-1⼀x+1-2⼀x^2+1-4⼀x^4+1-8⼀x^8+1..

2024-12-26 17:23:36

推荐回答（1个）

回答1：

1/x-1-1/x+1-2/x^2+1-4/x^4+1-8/x^8+1..
=(x+1-x+1)/(x²-1）-2/（x²+1)-4/(x⁴+1)-8/(x^8+1)...
=(2x²+2-2x²+2)/(x⁴-1)-4/(x⁴+1)-8/(x^8+1)
=(4x⁴+4-4x⁴+4)/(x^8-1)-8/(x^8+1)
=(8x^8+8-8x^8+8)/(x^16-1)
=16/(x^16-1)

1/x-1-1/x+1-2/x^2+1-4/x^4+1-8/x^8+1......-n/(xⁿ+1)
=(x+1-x+1)/(x²-1）-2/（x²+1)-4/(x⁴+1)-8/(x^8+1).........-n/(xⁿ+1)
=(2x²+2-2x²+2)/(x⁴-1)-4/(x⁴+1)-8/(x^8+1)......-n/(xⁿ+1)
=(4x⁴+4-4x⁴+4)/(x^8-1)-8/(x^8+1)......-n/(xⁿ+1)
=(8x^8+8-8x^8+8)/(x^16-1)......-n/(xⁿ+1)
=16/(x^16-1)......-n/(xⁿ+1)
=n/(xⁿ-1)