计算题 简算(-1/2)*2/3*(-3/4)*4/5*(-5/6)*······*(-19/20)(-1/2)-1/6-1/12-1/20-······-1/90

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计算题简算(-1/2)*2/3*(-3/4)*4/5*(-5/6)*······*(-19/20)(-1/2)-1/6-1/12-1/20-······-1/90计算题简算(-1/2)*2/3*(-3

计算题 简算(-1/2)*2/3*(-3/4)*4/5*(-5/6)*······*(-19/20)(-1/2)-1/6-1/12-1/20-······-1/90
计算题 简算
(-1/2)*2/3*(-3/4)*4/5*(-5/6)*······*(-19/20)
(-1/2)-1/6-1/12-1/20-······-1/90

计算题 简算(-1/2)*2/3*(-3/4)*4/5*(-5/6)*······*(-19/20)(-1/2)-1/6-1/12-1/20-······-1/90
第一题:负号数量为偶数,可直接去掉.分子分母互约,剩一头一尾,答案为1/20
第二题:分母拆分为相邻两数之积,负号提出,
原式=-(1/(1*2)+1/(2*3)+1/(3*4)+……+1/(9*10))
=-(1-1/2+1/2-1/3+1/3-1/4+……+1/9-1/10)
=-(1-1/10)
=-9/10

(1)1/20

(2)9/20

(-1/2)*2/3*(-3/4)*4/5*(-5/6)*······*(-19/20)
= 1/20
(-1/2)-1/6-1/12-1/20-······-1/90
= -[1/2+1/(2×3)+1/(3×4)+1/(4×5)+......+1/(9×10)]
= -[1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/9-1/10]
= -[1/2+1/2-1/10]
= -9/10

.....=1/20