อ้างอิง:
ข้อความเดิมเขียนโดยคุณ แฟร์
ถ้า (2^(1/2))*(4^(1/4))*(8^(1/8))*....*(1024^(1/1024)) สามารเขียนอยู่ในรูป 2^(2-(a/b))
โดยที่ a/b เป็นเศษส่วนอย่างดำ
แล้ว a - b + 1 มีด่าเท่าไร
(2^(1/2))*(2^(2/4))*(2^(3/8))*....*(2^(10/1024)) = 2^[ (1/2)+(2/4)+(3/8)+....+(10/1024) ]
2^[ (1/2)+(2/4)+(3/8)+....+(10/1024) ] = 2^(2-(a/b))
(1/2)+(2/4)+(3/8)+....+(10/1024) = 2-(a/b)) = S10
(1/2) S10 = (1/4)+(2/8)+(3/16)+....+(10/2048)
S10 - (1/2) S10 = (1/2) + ((2/4)-(1/4)) + ((3/8)-(2/8)) + .... + ((10/1024)-(9/1024)) - (10/2048)
(1/2) S10 = (1/2) + (1/4) + (1/8) + .... + (1/1024) - (10/2048)
(1/2) S10 = [ [ (1/2)( 1 - ((1/2)^10) ) ]/(1 - (1/2)) ] - (10/2048)
(1/2) S10 = 1 - (1/1024) - (10/2048)
S10 = 2 - (2/1024) - (20/2048) = 2 - (24/2048) = 2 - (3/256)
a = 3 , b = 256
a - b + 1 = 3 - 256 + 1 = -252 Answer
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งงตั้งแต่ตรงนี้เลยอะ
(1/2) S10 = [ [ (1/2)( 1 - ((1/2)^10) ) ]/(1 - (1/2)) ] - (10/2048)
(1/2) S10 = 1 - (1/1024) - (10/2048)
S10 = 2 - (2/1024) - (20/2048) = 2 - (24/2048) = 2 - (3/256)