Tính nhanh
A) (1-$\frac{1}{2}$ )x (1-$\frac{1}{3}$ )x (1-$\frac{1}{4}$ )x…x(1-$\frac{1}{10}$ )
B) $\frac{1}{2}$ + $\frac{1}{4}$ + $\frac{1}{8}$ + $\frac{1}{16}$ + $\frac{1}{32}$ + $\frac{1}{64}$
C) (1 + $\frac{1}{2}$) x (1+$\frac{1}{3}$) x (1+$\frac{1}{4}$) x… x (1+$\frac{1}{10}$
` a) `
` (1 – 1/2) × (1 – 1/3) × (1 – 1/4) × … × (1 – 1/10) `
` = 1/2 × 2/3 × 3/4 × … × 9/10 `
` = ` $\dfrac{1×2×3×…×9}{2×3×4×…×10}$
` = 1/10 `
` b) `
$\text{Đặt:}$
` A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 `
` A × 2 = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 `
` A × 2 – A = (1+1/2+1/4+1/8+1/16+1/32) – (1/2+1/4+1/8+1/16+1/32+1/64) `
` A = 1 – 1/64 `
` A = 63/64 `
` c) `
` (1 + 1/2) + (1 + 1/3) + (1 + 1/4) + … + (1 + 1/10) `
` = 3/2 + 4/3 + 5/4 + … + 11/10 `
` = ` $\dfrac{3×4×5×…×11}{2×3×4×…×10}$
` = ` $\dfrac{11}{2}$
$\text{@cindy}$
$\text{Xin hay nhất!!!}$
Đáp án + Giải thích các bước giải:
a)
`(1-1/2)xx(1-1/3)xx(1-1/4)xx…xx(1-1/10)`
`=1/2xx2/3xx3/4xx…xx9/10`
`=1/10`
b)
Đặt `A=1/2+1/4+1/8+…+1/64`
`=2xxA=2xx(1/2+1/4+1/8+…+1/64)`
`=2xxA=1+1/2+1/4+…+1/32`
`=2A-A=(1+1/2+1/4+…+1/32)-(1/2+1/4+1/8+…+1/64)`
`=A=1-1/64`
`=A=64/64-1/64`
`=A=63/64`
c)
`(1+1/2)xx(1+1/3)xx(1+1/4)…(1+1/10)`
`=3/2xx4/3xx5/4xx…xx11/10`
`=11/2`