1. Tính nhanh:
a, 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256
b, 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729
c, 1 + 5/4 + 5/8 + 5/16 + 5/32 + 5/64
Cần giải ra đầy đủ, dễ hiểu ạ
1. Tính nhanh: a, 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 b, 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 c, 1 + 5/4 + 5/8 + 5/16 + 5/32 + 5/6
By Melody
`a,`
Đặt:
`A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256`
`A xx 2 = 2 xx (1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256)`
`A xx 2 = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128`
`A xx 2 – A = (1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128) – (1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256)`
`A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 – 1/2 – 1/4 – 1/8 – 1/16 – 1/32 – 1/64 – 1/128 – 1/256`
`A = 1 – 1/256`
`A = 255/256`
`b,`
Đặt:
`B = 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729`
`3 xx B = 3 . (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729)`
`3 xx B = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243`
`3 xx B – B = (1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243) – (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729)`
`2 xx B = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 – 1/3 – 1/9 – 1/27 – 1/81 – 1/243 – 1/729`
`2 xx B = 1 – 1/729`
`2 xx B = 278/279`
`B = 278/279 : 2`
`B = 364/279`
`c,`
Đặt:
`C = 1 + 5/4 + 5/8 + 5/16 + 5/32 + 5/64`
`C = 5 xx (1/5 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64)`
Đặt:
`D = 1/5 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64`
`2 xx D = 2 xx (1/5 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64)`
`2 xx D = 2/5 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32`
`2 xx D – D = (2/5 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32) – (1/5 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64)`
`D = 2/5 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 – 1/5 – 1/4 – 1/8 – 1/16 – 1/32 – 1/64`
`D = 2/5 + 1/2 – 1/5 – 1/64`
`D = 1/5 + 1/2 – 1/64`
`D = 1/5 + 63/64`
`->` `C = 5 xx (1/5 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64)`
`C = 5 xx (1/5 + 63/64)`
`C = 1 + 315/64`
`C = 1 315/64`
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