Tính nhanh: a, A= 1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024 b, B=1/2+1/6 + 1/12+ 1/20+ 1/30+ 1/42+ 1/56

0 bình luận về “Tính nhanh: a, A= 1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024 b, B=1/2+1/6 + 1/12+ 1/20+ 1/30+ 1/42+ 1/56”

1. Đáp án:

    `a,A=1023/1024`

    `b,B=7/8`

   Giải thích các bước giải:

   `a,A= 1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024`

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

   `⇒2A=1+1/2+1/2^2+1/2^3+1/2^4+1/2^5+1/2^6+1/2^7+1/2^8+1/2^9`

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

   `⇒A=1-1/2^10`

   `⇒A=1-1/1024=1023/1024`

   `b, B=1/2+1/6 + 1/12+ 1/20+ 1/30+ 1/42+ 1/56 `

   `⇒B=1/1.2+1/2.3 + 1/3.4+ 1/4.5+ 1/5.6+ 1/6.7+ 1/7.8 `

   `⇒B=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 `

   `⇒B=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 `

   `⇒B=1+0+0+0+0+0+0-1/8 `

   `⇒B=1-1/8=7/8`

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2. Đáp án:

   `A=1023/1024`

   `B=7/8`

   Giải thích các bước giải:

   `a)“A=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024`

   `2A=2(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024)`

   `2A=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024`

   `2A-A=(1+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024)-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024)`

   `A=1-1/1024`

   `A=1023/1024`

   `b)“B=1/2+1/6+1/12+1/30+1/42+1/56`

   `B=1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8`

   `B=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`

   `B=1-1/8`

   `B=7/8`

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