Question

Bài 1 : Tính:

a)A=1.2+2.3+3.4+4.5+....+29.30

b) B=1+53+59+.....+599

c)12+22+32+.....302

Answer 1

a) \(A=1.2+2.3+3.4+...+29.30\)

\(\Rightarrow3A=1.2.3+2.3.\left(4-1\right)+3.4\left(5-2\right)+...+29.30\left(31-28\right)\)

\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+29.30.31-28.29.30\)

\(\Rightarrow3A=29.30.31\)

\(\Rightarrow A=29.30.31:3\)

\(\Rightarrow A=29.10.31\)

\(\Rightarrow A=8990\)

 

Answer 2

3A= 1.2.3+2.3.4+3.4.3 +......+ 29.30.3

3A= 1.2. ﴾3 ‐ 0﴿ + 2.3.﴾4 ‐ 1﴿ +3.4. ﴾5 ‐ 2﴿....... . 29.30. ﴾31 ‐ 28﴿

3A = ﴾1.2.3 + 2.3.4 + 3.4.5 +...... +18.20.21﴿ ‐ ﴾0.1.2 + 1.2.3 + 2.3.4 +.......+ 18.19.20﴿

3A = 29.30.31 ‐ 0.1.2

3A =26970‐0

3A= 26970

 A=26970:3

A = 8990.

Vậy A=8990