Toán Lớp 6: Cho T = 5 + $5^{2}$ + $5^{3}$ + … + $5^{2020}$ . Tìm số tự nhiên n sao cho 4 x T + 5 = $5^{n}$
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Toán Lớp 6: Cho T = 5 + $5^{2}$ + $5^{3}$ + … + $5^{2020}$ . Tìm số tự nhiên n sao cho 4 x T + 5 = $5^{n}$
Comments ( 2 )
=>5T=5( 5+5²+5³+…+5^2020)
=>5T=5²+5³+5⁴+…+5^2021
=>5T-T=(5²+5³+5⁴+…+5^2021)-(5+5²+5³+…+5^2020)
=>4T=5^2021 -5
=>T=(5^2021 -5)/4
=>4T+5=(5^2021 -5 )/4 . 4+5
=5^2021 – 5+5
=5^2021
=>5^n =5^2021
=>n=2021
Vậy n=2021