A=1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45-giúp em với ạ

2 bình luận về “A=1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45-giúp em với ạ”

1. Giải đáp:

    A=9/5

   Lời giải và giải thích chi tiết:

    A = 1 + 1/3 + 1/6 + 1/10 + 1/15 + 1/21 + 1/28 + 1/36 + 1/45

   1/2 xx A = 1/2 xx ( 1 + 1/3 + 1/6 + 1/10 + 1/15 + 1/21 + 1/28 + 1/36 + 1/45)

   A/2 = 1 xx 1/2 + 1/3 xx 1/2 + 1/6 xx 1/2 + 1/10 xx 1/2 + 1/15 xx 1/2 + 1/21 xx 1/2 + 1/28 xx 1/2 + 1/36 xx 1/2 + 1/45 xx 1/2

   A/2 = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90

   A/2 = 1/(1xx2) + 1/(2xx3) + 1/(3xx4) +1/(4xx5) +1/(5xx6) +1/(6xx7) + 1/(7xx8) + 1/(8xx9) + 1/(9xx10)

   A/2 = 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/2 = 1 – 1/10

   A/2 = 10/10 – 1/10

   A/2 = 9/10

   A = 9/10 : 1/2

   A = 9/10 xx 2

   A = 9/5

   Vậy A = 9/5

   ———-

   Áp dụng:

   1/(nxx(n+1)) = 1/n – 1/(n+1)

   Trả lời
2. A= 1 + 1/3 + 1/6 +1/10 + 1/15 + 1/21 + 1/28 + 1/36 + 1/45

   1/2 x A= (1 + 1/3 +1/6 + 1/10 + 1/15 + 1/21 + 1/28 + 1/36 + 1/45) x 1/2

   1/2 x A= 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 +1/56 + 1/72 + 1/90

   1/2 x A = 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

   1/2 x A = 1/1-1/2+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

   1/2xA= 1/1 – 1/10 = 9/10

   A= 9/10 : 1/2 = 18/10 = 9/5

   Trả lời