Question

TÍNH TỔNG DÃY SAU:

\(C=1\times2+2\times3+3\times4+...+99\times100\)

Answer 1

      C=1x2+2x3+3x4 +......+99x100

<=>3xC=1x2x3+2x3x3+.....+99x100x3

<=>3xC=1x2x3+2x3x(4-1)+.....+99x100x(101-98)

<=>3xC=1x2x3-1x2x3+2x3x4-2x3x4+......-98x99x100+99x100x101

<=>3xC=99x100x101   <=> C=99x100x101 :3    <=> C= 333300

Answer 2

\(C=1.2+2.3+3.4+...+99.100\)

=> 3C = 1.2.3 + 2.3.3 + 3.4.3 + ...+ 99.100.3

3C = 1.2.3 + 2.3.(4-1) + 3.4.(5-2) + ...+ 99.100.(101-98)

3C = 1.2.3 + 2.3.4 -1.2.3 + 3.4.5 - 2.3.4 + ...+ 99.100.101-98.99.100

\(3C=\left(1.2.3+2.3.4+3.4.5+...+99.100.101\right)-\left(1.2.3+2.3.4+...+98.99.100\right)\)

\(3C=99.100.101\Rightarrow C=\frac{99.100.101}{3}=333300\)

Dấu . là dấu nhân

3C = 3 x C

Answer 3

C = 1 x 2 + 2 x 3 + 3 x 4 + ....+ 99 x 100

C x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + .. + 99x100x3

C x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)

C x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100

C x 3 = 99 x 100 x101

C = 99 x 100 x 101 : 3

C = 333 300