数学的化简题(2根号1)+(根号2)分之1+(3根号2)+(2根号3)分之1+······+(1

问题描述:

数学的化简题(2根号1)+(根号2)分之1+(3根号2)+(2根号3)分之1+······+(1
(2根号1)+(根号2)分之1+(3根号2)+(2根号3)分之1+······+(100根号99)+(99根号100)分之1

原式=(√3-√2)×(√3)/(√2-1)-1
=(√3-√2)×√3×(√2+1)/[(√2+1)(√2-1)]-1
=(√3×√3-√2×√3)(√2+1)/(√2²-1)-1
=(3-√6)(√2+1)/(2-1)-1
=3×√2+3×1-√6×√2-√6×1-1
=√6+3-√12-√6-1
=√6+3-2√3-√6-1
=2-2√3