\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{29\cdot30}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{29}-\frac{1}{30}\)

\(=1-\frac{1}{30}\)

\(=\frac{29}{30}\)

cảm ơn bạn nha

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{29\cdot30}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{29}-\frac{1}{30}\)

\(=1-\frac{1}{30}=\frac{29}{30}\)

a/ \(3A=1.2.3+2.3.3+3.4.3+4.5.3+...+29.30.3.\)

\(3A=1.2.3+2.3\left(4-1\right)+3.4.\left(5-2\right)+4.5\left(6-3\right)+...+29.30\left(31-28\right)\)

\(3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+...+29.30.31-28.29.30\)

\(3A=29.30.31\Rightarrow A=\frac{29.30.31}{3}=10.29.31=8990\)

c/ \(C=1+2\left(1+1\right)+3\left(2+1\right)+4\left(3+1\right)+...+30\left(29+1\right)\)

\(C=1+2+1.2+2.3+3+3.4+4+...+29.30+30\)

\(C=\left(1+2+3+4+...+30\right)+\left(1.2+2.3+3.4+...+29.30\right)\)

Dấu ngoặc thứ nhất là tính tổng 1 cấp số cộng, dấu ngoặc thứ 2 chính là câu a

b/ Câu b dãy viết ngắn quá chưa tìm ra quy luật

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

=> 3A = 1.2.3 + 2.3.(4-1) + ... + 29.30.(31-28)

          = 1.2.3 + 2.3.4 - 1.2.3 + ... + 29.30.31 - 28.29.30

          = 29.30.31

=> A = \(\frac{29.30.31}{3}=8990\)

a) \(A=1.2+2.3+3.4+...+29.30\)

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

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

\(\Rightarrow3A=29.30.31\)

\(\Rightarrow A=29.30.31:3\)

\(\Rightarrow A=29.10.31\)

\(\Rightarrow A=8990\)

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

cau hỏi tương tự ko có mà!!!!!!!!!!!!!!!!!!!!!!!!!!!!

3C=1.2.3+2.3.(4-1)+3.4.(5-2)+...+2014.2015.(2016-2013)

3C=2014.2015.2016

C=2014.2015.2016:3

Ta có : S = 1.2 + 2.3 + 3.4 + ..... + 32.33

=> 3S = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ...... + 32.33.34

=> 3S = 32.33.34

=> S = \(\frac{32.33.34}{3}=11968\)

C=1*2+2*3+3*4+...+98*99

C=2+6+12+...+9702

C=2+9702

C=9704

vay C=9704

D=(1*99+2*99+3*99+...+99*99)-(1*2+2*3+3*4+...+98*99)

D=(99+198+297+...+9801)-(2+6+12+...+9702)

D=(99+9801)-(2+9702)

D=9900-9704

D=196

vay D=196

ai di qua dong tinh thi nho h cho minh nhe