巧算:(3+1)(3的2次方+1)(3的4次方+1)(3的5次方+1)......(3的2n次方+1)
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巧算:(3+1)(3的2次方+1)(3的4次方+1)(3的5次方+1)......(3的2n次方+1)
巧算:(3+1)(3的2次方+1)(3的4次方+1)(3的5次方+1)......(3的2n次方+1)
巧算:(3+1)(3的2次方+1)(3的4次方+1)(3的5次方+1)......(3的2n次方+1)
题目应该是这样的:
原式的=
2(3+1)(3^2 +1)(3^4 +1)(3^8 +1).(3^2n+1)/2
=(3-1)(3+1)(3^2 +1)(3^4 +1).(3^2n+1)/2
=(3^2-1)(3^2+1)(3^4+1).(3^2n+1)/2
=(3^4-1)(3^4+1)(3^8+1).(3^2n+1)/2
=.
=(3^4n-1)/2
(3+1)(3^2+1)(3^4+1)(3^8+1)...(3^2n+1)
=(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)...(3^2n+1)/(3-1)
=(3²-1)(3^2+1)(3^4+1)(3^8+1)...(3^2n+1)/2
=(3^4-1)(3^4+1)(3^8+1)...(3^2n+1)/2
=(3^2n-1)(3^2n+1)/2
=(3^4n-1)/2