Toán Lớp 6: Rút gọn S
S=1+3+3^2+3^3+…+3^99+3^100
Chứng mình S chia hết cho 4
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Toán Lớp 6: Rút gọn S
S=1+3+3^2+3^3+…+3^99+3^100
Chứng mình S chia hết cho 4
Comments ( 2 )
S=1+3+3^2+3^3+…+3^99
=>3S=3+3^2+3^3+3^4+…+3^100
=>3S-S=(3+3^2+3^3+3^4+…+3^100)-(1+3+3^2+3^3+…+3^99)
=>2S=3^100-1
=>S=[3^100-1]/2
Vậy S=[3^100-1]/2
S=1+3+3^2+3^3+…+3^99
S=(1+3)+(3^2+3^3)+…+(3^98+3^99)
S=1.(1+3)+3^2(1+3)+…+3^98(1+3)
S=1. 4+3^2. 4+…+3^98. 4
S=4(1+3^2+…+3^98)\vdots4
Vậy S \vdots4