Toán Lớp 6: Cho A = 3+3^2+3^3+3^4+…+3^100
Tìm số tự nhiên n, biết 2A + 3 = 3^4n+1
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Toán Lớp 6: Cho A = 3+3^2+3^3+3^4+…+3^100
Tìm số tự nhiên n, biết 2A + 3 = 3^4n+1
Comments ( 2 )
=>3A=3(3+3²+3³+3⁴+…+3^100)
=>3A=3²+3³+3⁴+3⁵+…+3^101
=>3A-A=(3²+3³+3⁴+3⁵+…+3^101) -(3+3²+3³+3⁴+…+3^100)
=>2A=3^101 -3
=>2A+3 =3^101 -3+3
=>2A+3=3^101
Mà 2A+3=3^(4n+1)
=>3^101 =3^(4n+1)
=>101=4n+1
=>4n=101-1
=>4n=100
=>n=100/4
=>n=25
Vậy n=25