Toán Lớp 6: Rút gọn:
A=1/2+1/2^2+1/2^3+…+1^2^100
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Toán Lớp 6: Rút gọn:
A=1/2+1/2^2+1/2^3+…+1^2^100
Comments ( 2 )
2A=2.(1/2+1/2^2+1/2^3+…+1/2^100)
2A=2/2+2/2^2+2/2^3+…+2/2^100
2A=1+1/2+1/2^2+…+1/2^99
2A-A=(1+1/2+1/2^2+…+1/2^99)-(1/2+1/2^2+1/2^3+…+1/2^100)
A=1+1/2+1/2^2+…+1/2^99-1/2-1/2^2-1/2^3-…-1/2^100
A=1+(1/2-1/2)+(1/2^2-1/2^2)+(1/2^3-1/2^3)+…(1/2^99-1/2^99)-1/2^100
A=1-1/2^100
A=2^100/2^100-1/2^100
A=(2^100-1)/(2^100)
Vậy A=(2^100-1)/(2^100)
2A=1+1/2+1/2^3+…+1/2^99
2A-A=(1+1/2+1/2^3+…+1/2^99)-(1/2+1/2^2+1/2^3+…+1/2^100)
A=1-1/2^100
A=[2^100-1]/2^100
Vậy A=[2^100-1]/2^100