Toán Lớp 6: $\frac{1}{2}$ + $\frac{3}{2}$ + $\frac{3}{2}${2}$ +………..+ ($\frac{3}{2}$) ^2021
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Toán Lớp 6: $\frac{1}{2}$ + $\frac{3}{2}$ + $\frac{3}{2}${2}$ +………..+ ($\frac{3}{2}$) ^2021
Comments ( 1 )
Giải đáp:
(3^2022)/(2^2021) -5/2
Lời giải và giải thích chi tiết:
Đặt A =3/2 +(3/2)^2+… +(3/2)^2021
=> 3/2A= (3/2)^2+ (3/2)^3+ … +(3/2)^2021+(3/2)^2022
=> 3/2A – A = [ (3/2)^2+ (3/2)^3+ … +(3/2)^2021+(3/2)^2022] -[3/2 +(3/2)^2+… +(3/2)^2021]
=> 1/2A =(3/2)^2022 -3/2
=> A = [(3/2)^2022 -3/2] : 1/2 = 2[(3/2)^2022 -3/2] = (2 . 3^2022)/(2^2022) – 3 = (3^2022)/(2^2021) -3
Suy ra :
1/2 + 3/2 +(3/2)^2+… +(3/2)^2021
= 1/2 + (3^2022)/(2^2021) -3
= (3^2022)/(2^2021) -5/2