Question

1. tính nhanh

3/ 1  +  3/1+2  +  3/1+2+3  +  3/1+2+3+4  +  ... +  3/1+2+3+4+...+100

Answer 1

3/1 + 3/1+2 + 3/1+2+3 + 3/1+2+3+4 + ... + 3/1+2+3+4+...+100

= 3 × (1/0+1 + 1/1+2 + 1/1+2+3 + 1/1+2+3+4 + ... + 1/1+2+3+4+...+100)

= 3 × (1/(1+0)×2:2 + 1/(1+2)×2:2 + 1/(1+3)×3:2 + 1/(1+4)×4:2 + ... + 1/(1+100)×100:2)

= 3 × (2/1×2 + 2/2×3 + 2/3×4 + 2/4×5 + ... + 2/100×101)

= 3 × 2 × (1/1×2 + 1/2×3 + 1/3×4 + 1/4×5 + ... + 1/100×101)

= 6 × (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/100 - 1/101)

= 6 × (1 - 1/100)

= 6 × 100/101

= 600/101

Answer 2

không biết làm

Answer 3

3/1 + 3/1+2 + 3/1+2+3 + ..................... + 3/1+2+3+4+ ...+100

= 3 x [1/1 + 1/1x3 +1/2x3 +1/2x5 +1/3x5 +1/3x7 + ... 1/50 x 99 +1/50 x 101]

= 3 x [1/1 x (1/1+1/3) +1/2 x (1/3+1/5) +  1/3 x(1/5+1/7) + ... + 1/50 x (1/99+1/101)

= 3 x (4/1x3 +4/3x5 +4/5x7 + ... 4/99x101)

= 3 x [(4/1 -4/3 +4/3 -4/5 +4/5 -4/7+...4/99 -4/101) : 2]

= 3 x [(4/1-4/101) :2]

= 3 x 200/101

= 600/101