Giúp mik với mik cần gấp A=1\2 + 5\6 + 11\12 + 19\20 + 29\30 + 41\42 + 55\56 + 71\72 + 89\90 Tính tổng nha

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1. `A=1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90`

   `→A=(1-1/2) + (1-1/6 )+ (1-1/12) + (1-1/20) + (1-1/30) + (1-1/42) + (1-1/56) + (1-1/72) + (1-1/90)`

   `→A=(1+1+1+1+1+1+1+1+1)-(1/2+ 1/6 + 1/12 + 1/20+ 1/30 + 1/42+ 1/56+ 1/72+ 1/90)`

    Đặt `B=1/2+ 1/6 + 1/12 + 1/20+ 1/30 + 1/42+ 1/56+ 1/72+ 1/90`

   `→B=1/(1×2)+ 1/(2×3) + 1/(3×4) + 1/(4×5)+ 1/(5×6) + 1/(6×7)+ 1/(7×8)+ 1/(8×9)+ 1/(9×10)`

   `→B=1-1/2+1/2-1/3+….+1/9-1/(10)`

   `→B=1-1/(10)=9/(10)`

   Ta có: `A=(1+1+1+1+1+1+1+1+1)-B`

   `→A=9-9/(10)=(81)/(10)`.

   Trả lời

2. `A=1/2+5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90`

   `⇒A=(1-1/2)+(1-1/6)+(1-12)+(1-1/20)+(1-1/30)+(1-1/42)+(1-1/56)+(1-1/72)+(1-1/90)`

   `⇒A=9-(1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)`

   `⇒A=9-(1/{1×2}+1/{2×3}+1/{3×4}+1/{4×5}+1/{5×6}+1/{6×7}+1/{7×8}+1/{8×9}+1/{9×10})`

   `⇒A=9-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)`

   `⇒A=9-(1-1/10)`

   `⇒A=9-9/10`

   `⇒A=81/10`

   Trả lời