1.2+2.3+3.4+....+29.30
1/1.2+1/2.3+1/3.4+...1/29.30
\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{29\cdot30}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{29}-\frac{1}{30}\)
\(=1-\frac{1}{30}\)
\(=\frac{29}{30}\)
\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{29\cdot30}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{29}-\frac{1}{30}\)
\(=1-\frac{1}{30}=\frac{29}{30}\)
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
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
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
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 = \(\frac{29.30.31}{3}=8990\)
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
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
Tính nhanh
C=1.2+2.3+3.4+...+2014.2015
K=1.2+2.3+3.4+..+(n-1).n
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
Tính
a) S= 1.2+2.3+3.4+...+32.33
b) S= 1.2+2.3+3.4+...+49.50
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 = \(\frac{32.33.34}{3}=11968\)
Tính các biểu thức sau:
C=1.2+2.3+3.4+...+98.99
D=(1.99+2.99+3.99+...99.99)-(1.2+2.3+3.4+...98.99
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
\(\left(1-\frac{1}{1.2}\right)+\left(1-\frac{1}{2.3}\right)+...+\left(1-\frac{1}{29.30}\right)\)
Cho A=1/1.2 + 1/2.3 + + 1/ 3.4+...+1/49.50 ; B = 1.2+2.3+3.4+4.5+5.6+...+49.50
Tính 50 mủ 2 A – B/17