so sánh a=2/3+14/15+34/35+62/63+98/99+142/143+194/195 với b=5-1/2^2+1/3^3+1/4^4+1/5^5+1/6^6+1/7^7

0 bình luận về “so sánh a=2/3+14/15+34/35+62/63+98/99+142/143+194/195 với b=5-1/2^2+1/3^3+1/4^4+1/5^5+1/6^6+1/7^7”

1. Ta có :

   A =( 1 – 1/3) + (1-1/15) +( 1- 1/35) +(1-1/63) + (1-1/99) +(1-1/143) -(1-1/195) =7 – ( 1/3 + 1/15 + 1/35 + 1/63 + 1/99 + 1/143 + 1/195 ) = 7 – 1/2.( 1/1.3 + 1/3.5 + 1/5.7 + 1/7.9 + 1/9.11 + 1/11.13 + 1/13.15 ) = 7 – 1/2. (1 – 1/15 ) = 7 – 1/2 .14/15 = 98/15 > 75/15 = 5 (1)

   B=5-1/2^2+1/3^3+1/4^4+1/5^5+1/6^6+1/7^7 < 5 (2)

   Từ (1),(2) ⇒ A > 5 >B ⇒A > B

   Chúc bạn học tốt nhé 

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2. Đáp án:

   `A>B`

   Giải thích các bước giải:

   `A=2/3+14/15+34/35+62/63+98/99+142/143+194/195`

   `=>A=(1-1/3)+(1-1/15)+(1-1/35)+(1-1/63)+(1-1/99)+(1-1/143)+(1/195)`

   `=>A=7-(1/3+1/15+1/35+1/63+1/99+1/143+1/195`

   `=>A=7-(1/1.3+1/3.5+1/5.7+1/7.9+1/9.11+1/11.13+1/13.15)`

   `=>A=7-1/2(2/1.3+2/3.5+2/5.7+2/7.9+2/9.11+2/11.13+2/13.15)`

   `=>A=7-1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)`

   `=>A=7-1/2(1-1/15)`

   `=>A=7-1/2*14/15`

   `=>A=7-7/15>6` (Vì `7/15∉N text(*)`)

   `B=5-1/2^2+1/3^3+1/4^4+1/5^5+1/6^6+1/7^7`

   `=>B=5-(1/2^2+1/3^3+1/4^4+1/5^5+1/6^6+1/7^7)`

   `=>B<5`

   `=>A>6>5>B`

   Vậy `A>B`.

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