S = 3 + 2^2 – 2^3+ 2^4 – … – 2^99 + 2^100

2 bình luận về “S = 3 + 2^2 – 2^3+ 2^4 – … – 2^99 + 2^100”

1. Giải đáp + Lời giải và giải thích chi tiết:

   S = 3 + 2^2 – 2^3 + 2^4 – … – 2^99 + 2^100

   2S = 6 + 2^3 – 2^4 + 2^5 – … – 2^100 + 2^101

   2S + S = (6 + 2^3 – 2^4 + 2^5 – … – 2^100 + 2^101) + ( 3 + 2^2 – 2^3 + 2^4 – … – 2^99 + 2^100)

   3S = 6 + 2^3 – 2^4 + 2^5 – … – 2^100 + 2^101 + 3 + 2^2 – 2^3 + 2^4 – … – 2^99 + 2^100

   3S = 9 + 2^2 + 2^101

   S = (9 + 2^2 + 2^101)/3.

   Trả lời
2. Ta có :

   S = 3 + 2^2 – 2^3 + 2^4 – … – 2^99 + 2^100

   2S = 6 + 2^3 – 2^4 + 2^5 – … – 2^100 + 2^101

   2S + S = (6 + 2^3 – 2^4 + 2^5 – … – 2^100 + 2^101) + (3 + 2^2 – 2^3 + 2^4 – … – 2^99 + 2^100)

   S(2+1) = 6 + 2^3 – 2^4 + 2^5 – … – 2^100 + 2^101 + 3 + 2^2 – 2^3 + 2^4 – … – 2^99 + 2^100

   S.3 = 2^2 + 2^101 + 9 

   S = (2^2 + 2^101 + 9) : 3

   Trả lời