Toán Lớp 6: A=10¹⁰⁰-10⁹⁹+10⁹⁸-10⁹⁷+…+10²-10¹+1 mình cần gấp
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Toán Lớp 6: A=10¹⁰⁰-10⁹⁹+10⁹⁸-10⁹⁷+…+10²-10¹+1 mình cần gấp
Comments ( 2 )
A = 10^100 – 10^99 + 10^98 – 10^97 + … + 10^2 – 10^1 +1
=> 10A = 10^101 – 10^100 + 10^99 – 10^98 + … + 10^3 – 10^2 + 10
=> 10A + A = ( 10^101 – 10^100 + 10^99 – 10^98 + … + 10^3 – 10^2 + 10^1 ) +( 10^100 – 10^99 + 10^98 – 10^97 + … + 10^2 – 10^1 +1 )
=> 11A = 10^101 – 1
=> A = {10^101 – 1}/11
Vậy A = {10^101 -1}/11
#dtkc
Lời giải và giải thích chi tiết:
A = 10^100 – 10^99 + 10^98 – 10^97 + ………… + 10^2 – 10^1 + 1
10A = 10^101 – 10^100 + 10^99 – 10^98 + ………. + 10^3 – 10^2 + 10^1
10A + A = (10^101 – 10^100 + ………. + 10^1) + (10^100 – 10^99 + ……… + 1)
11A = 10^101 + 1
A = (10^101 + 1)/11