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(5+6)/5x6-(6+7)/6x7+(7+8)/7x8-(8+9)/8x9+(9+10)/9x10
题目详情
(5+6)/5x6-(6+7)/6x7+(7+8)/7x8-(8+9)/8x9+(9+10)/9x10
▼优质解答
答案和解析
(5+6)/5x6=1/5+1/6,
(6+7)/6x7=1/6+1/7
(7+8)/7x8=1/7+1/8,
(8+9)/8x9=1/8+1/9
(9+10)/9x10=1/9+1/10
∴(5+6)/5x6-(6+7)/6x7+(7+8)/7x8-(8+9)/8x9+(9+10)/9x10
=1/5+1/6-(1/6+1/7)+(1/7+1/8)-(1/8-1/9)+(1/9+1/10)
=1/5+1/10
=3/10.
(6+7)/6x7=1/6+1/7
(7+8)/7x8=1/7+1/8,
(8+9)/8x9=1/8+1/9
(9+10)/9x10=1/9+1/10
∴(5+6)/5x6-(6+7)/6x7+(7+8)/7x8-(8+9)/8x9+(9+10)/9x10
=1/5+1/6-(1/6+1/7)+(1/7+1/8)-(1/8-1/9)+(1/9+1/10)
=1/5+1/10
=3/10.
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