数学题1/42+1/56+1/78+1/90+1/110+1/132计算过程、得数!
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![数学题1/42+1/56+1/78+1/90+1/110+1/132计算过程、得数!](/uploads/image/z/101254-22-4.jpg?t=%E6%95%B0%E5%AD%A6%E9%A2%981%2F42%2B1%2F56%2B1%2F78%2B1%2F90%2B1%2F110%2B1%2F132%E8%AE%A1%E7%AE%97%E8%BF%87%E7%A8%8B%E3%80%81%E5%BE%97%E6%95%B0%21)
数学题1/42+1/56+1/78+1/90+1/110+1/132计算过程、得数!
数学题1/42+1/56+1/78+1/90+1/110+1/132计算过程、得数!
数学题1/42+1/56+1/78+1/90+1/110+1/132计算过程、得数!
丿Smile丶沫 ,
1/42+1/56+1/72+1/90+1/110+1/132
=(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/10-1/11)+(1/11-1/12)
=1/6-1/12
=1/12
1/42+1/56+1/78+1/90+1/110+1/132?
因该是1/42+1/56+1/72+1/90+1/110+1/132吧
1/42+1/56+1/72+1/90+1/110+1/132
=1/(6×7)+1/(7×8)+1/(8×9)+1/(9×10)+1/(10×11)+1/(11×12)
=1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11+1/11-1/12
=1/6-1/12
=1/12
1/[n×(n+1)]=1/n-1/(n+1)
所以原式=1/6 - 1/7 + 1/7 - 1/8 + …… + 1/11 - 1/12 =1/6 - 1/12 = 1/12
=1/6*7+1/7*8+1/8*9+1/9*10+1/10*11+1/11*12=1/6-1/12=1/12
1/78 应为1/72
1/42+1/56+1/72+1/90+1/110+1/132 78应为72
=(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)+(1/10-1/11)+(1/11-1/12)
=1/6-1/12
=1/12
=1/6-1/12=1/12分成两个数的乘积裂项相消