Cho B = 1.2 + 2.3 + 3.4 + …..+ 31.32 + 32.33. Chứng tỏ rằng B ⋮ 34.

Lời giải:

Ta có: B = 1.2 + 2.3 + 3.4 + …..+ 31.32 + 32.33.

3B = 1.2.3 + 2.3.3 + 3.4.3 + …..+ 31.32.3 + 32.33.3

= 1.2.3 + 2.3.(4 – 1) +…….+ 31.32.(33 – 30) + 32. 33.(34 – 31)

= 1.2.3 + 2.3.4 – 2.3.1 +……+ 31.32.33 – 31.32.30 + 32.33.34 – 32.33.31

= 32.33.24

Suy ra B = \(\frac{{32.33.34}}{3} = 32.11.34\).

Mà 34 ⋮ 34 nên B = 32.11.34 ⋮ 34.