
2(3+1)(3的平方+1)(3的4次方+1)(3的8次方+1)+1。 要算式,
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2(3+1)(3^2+1)(3^4+1)(3^8+1)...(3^2n+1)
=2(3^2-1)(3^2+1)(3^4+1)(3^8+1)...(3^2n+1)/(3-1)
=2(3^4-1)(3^4+1)(3^8+1)...(3^2n+1)/(3-1)
=2(3^8-1)(3^8+1)...(3^2n+1)/(3-1)
=2(3^16-1)...(3^2)^n+1)/(3-1)
=2[(3^2)^2n+1]/2
=(81^n +1)
=2(3^2-1)(3^2+1)(3^4+1)(3^8+1)...(3^2n+1)/(3-1)
=2(3^4-1)(3^4+1)(3^8+1)...(3^2n+1)/(3-1)
=2(3^8-1)(3^8+1)...(3^2n+1)/(3-1)
=2(3^16-1)...(3^2)^n+1)/(3-1)
=2[(3^2)^2n+1]/2
=(81^n +1)
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