` 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 `
` = ` $\dfrac{3×4×5×...×11}{2×3×4×...×10}$
` = ` $\dfrac{11}{2}$
$\text{@cindy}$
$\text{Xin hay nhất!!!}$