Question

P=1×2+2×3+3×4+ ... + 99×100

Answer 1

P = 1 × 2 + 2 × 3 + 3 × 4 +  ...  + 99 × 100

3P = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ..... + 99.100.101

3P = 99.100.101

P = 99.100.101/3

P = 333300

Answer 2

P = 1×2 + 2×3 + 3×4 + ... + 99×100

3P = 1×2×(3-0) + 2×3×(4-1) + 3×4×(5-2) + ... + 99×100×(101-98)

3P = 1×2×3 - 0×1×2 + 2×3×4 - 1×2×3 + 3×4×5 - 2×3×4 + ... × 99×100×101 - 98×99×100

3P = (1×2×3 + 2×3×4 + 3×4×5 + ... + 99×100×101) - (0×1×2 + 1×2×3 + 2×3×4 + ... + 98×99×100)

3P = 99×100×101 - 0×1×2

3P = 99×100×101

P = 33×100×101

P = 333300

Answer 3

P=1x2+2x3+3x4+...+99x100

Px3=1x2x3+2x3x3+3x4x3+...+99x100x3

Px3=1x2x3+2x3x(4-1)+3x4x(5-2)+...+99x100x(101-98)

Px3=1x2x3+2x3x4-1x2x3+3x4x5-2x3x4+...+99x100x101-98x99x100

Px3=(1x2x3-1x2x3)+(2x3x4-2x3x4)+(3x4x5-3x4x5)+...(98x99x100-98x99x100)+99x100x101

Px3=0+0+0+...+0+99x100x101

Px3=99x100x101

P=99x100x101:3

P=999900:3

P=333300

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