Question

Biết: S=2.3+3.4+4.5+...+34.35. Kết quả của tổng trên. Làm giúp mk nha mk.

Answer 1

S=2.3+3.4+4.5+....+34.35

3S=2.3.3+3.4.3+4.5.3+...+34.35.3

3S=2.3.(4−1)+3.4.(5−2)+4.5.(6−3)+...+34.35.(36−33)

3S=2.3.4−1.2.3+3.4.5−2.3.4+4.5.6−3.4.5+....+34.35.36−33.34.35

3S=34.35.36−6

S=\(\frac{\text{34.35.36−6}}{3}\)

Answer 2

\(3S=3x2x3+3x3x4+..+3x34x35\)

\(3S=3x2\left(4-1\right)\)\(+3x3\left(5-1\right)\)\(+...+34x35\left(36-33\right)\)

\(3S=3x2x4-1x2x3+3x4x5-2x3x4+...+34x35x36-33x34x35\)

\(3S=34x35x36-6\)

\(3S=42834\)

\(S=42834:3=14278\)