Số đó là 60.

  l ike cho mình nhé !

.

mình theo Giang

Đặt A1 = 1/2^1 + 1/2^2 + ... + 1/2^100 
A2 = 1/2^2 + 1/2^3 + ... + 1/2^100 
A3 = 1/2^3 + 1/2^4 + ... + 1/2^100 
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A100 = 1/2^100 
A = 1/2^1 + 2/2^2 + 3/2^3 + 4/2^4 + ... + 100/2^100 = 
= (1/2^1+1/2^2 +...+ 1/2^100) + (1/2^2+1/2^3 +...+ 1/2^100) + (1/2^3+1/2^4 +...+ 1/2^100) + ... + (1/2^100) = A1 + A2 + A3 + ... + A100 
2^101 A1 = 2^100 + 2^99 + 2^98 + ... + 2 (1) 
2^100 A1 = 2^99 + 2^98 + 2^97 + ... + 1 (2) 
(2) trừ (1) ---> 2^100 A1 = 2^100 - 1 ---> A1 = (2^100 - 1) / 2^100 = 1 - 1/2^100 
Tương tự 
2^101 A2 = 2^99 + 2^98 + 2^97 +...+ 2 (3) 
2^100 A2 = 2^98 + 2^97 + 2^96 +...+ 1 (4) 
(4) trừ (3) ---> 2^100 A2 = 2^99 - 1 ---> A2 = (2^99 - 1) / 2^100 = 1/2 - 1/2^100 
Tương tự 
A3 = 1/4 - 1/2^100 = 1/2^2 - 1/2^100 
A4 = 1/2^3 - 1/2^100 
.................................. 
................................. 
A100 = 1/2^99 - 1/2^100 
Vậy A = A1 + A2 + A3 +...+ A100 = (1 + 1/2 + 1/2^2 + ... + 1/2^99) - 100/2^100 
= 2 A1 - 100/2^100 = 2 - 2/2^100 - 100/2^100 = 2 - 51/2^99 

Nguồn: TÝnh: A = 1 + 3/2^3 + 4/2^4 +5/2^5 + ....+100/2^100? Ai tra loi dung cho 5 sao? | Yahoo Hỏi & Đáp