Question

(1-x)分之1+(1+x)分之1+(1+x^2)分之2+(1+X^4)分之4+(1+x^8)分之8+(1+x^16)分

Answer 1

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1/(1-x) + 1/(1+x) + 2/(1+x²)+4/(1+x⁴)+8/(1+x^8) + 16/(1+x^16) + 32/(1+x^32)

= 2/(1-x²) + 2/(1+x²) +4/(1+x⁴)+8/(1+x^8) + 16/(1+x^16) + 32/(1+x^32)

= 4/(1-x⁴) +4/(1+x⁴)+8/(1+x^8) + 16/(1+x^16) + 32/(1+x^32)

= 8/(1-x^8) +8/(1+x^8) + 16/(1+x^16) + 32/(1+x^32)

= 16/(1-x^16) + 16/(1+x^16) + 32/(1+x^32)

= 32/(1-x^32) + 32/(1+x^32)

= 64/(1 - x^64)