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NB
2
5 tháng 4 2016
S = 1x2 + 2x3 + 3x4 + ……………… + 11x12 + 12x13
3S=1x2x3 + 2x3x3 + 3x4x3+ ………. + 11x12x3 + 12x13x3
Ta lấy K = 1x2x3 +2x3x4 + 3x4x5 + …… + 11x12x13 + 12x13x14
- 3S = 1x2x3 + 2x3x3 + 3x4x3+ ……… + 11x12x3 + 12x13x3
------------------------------------------------------------------------------------
K – 3S = 0 + 2x3x1 + 3x4x2 + …… .. + 11x12x10 + 12x13x11
K – 3S = K – 12x13x14
Từ đó suy ra: 3S = 12x13x14
S = 4x13x14 = 728
Cách 2:
S x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + …. + 11x12x(13-10) + 12x13x(14-11)
S x 3 = 1x2x3 + 2x3x4 – 2x3x1 + 3x4x5 – 3x4x2 + …..+ 11x12x13 – 11x12x10 +12x13x14 – 12x13x11
S x 3 = 12 x 13 x14
S = 4 x 13 x 14
S = 728
ai k minh minh k lai cho
NT
3
8 tháng 4 2016
S = 1x2 + 2x3 + 3x4 + ……………… + 11x12 + 12x13
3S=1x2x3 + 2x3x3 + 3x4x3+ ………. + 11x12x3 + 12x13x3
Ta lấy K = 1x2x3 +2x3x4 + 3x4x5 + …… + 11x12x13 + 12x13x14
- 3S = 1x2x3 + 2x3x3 + 3x4x3+ ……… + 11x12x3 + 12x13x3
------------------------------------------------------------------------------------
K – 3S = 0 + 2x3x1 + 3x4x2 + …… .. + 11x12x10 + 12x13x11
K – 3S = K – 12x13x14
Từ đó suy ra: 3S = 12x13x14
S = 4x13x14 = 728
DP
26 tháng 6 2017
Bài 3 :
\(A=\frac{1}{1\times2}+\frac{1}{2\times3}+....+\frac{1}{99\times100}\)
Ta có : \(\frac{1}{1\times2}=\frac{2-1}{1\times2}=\frac{2}{1\times2}-\frac{1}{1\times2}=1-\frac{1}{2}\)
\(\frac{1}{2\times3}=\frac{3-2}{2\times3}=\frac{3}{2\times3}-\frac{2}{2\times3}=\frac{1}{2}-\frac{1}{3}\)
\(\frac{1}{99\times100}=\frac{100-99}{99\times100}=\frac{100}{99\times100}-\frac{99}{99\times100}=\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}\)
\(A=\frac{99}{100}\)
\(B=\frac{1}{10\times11}+\frac{1}{11\times12}+...+\frac{1}{38\times39}\)
Ta có : \(\frac{1}{10\times11}=\frac{11-10}{10\times11}=\frac{11}{10\times11}-\frac{10}{10\times11}=\frac{1}{10}-\frac{1}{11}\)
\(\frac{1}{11\times12}=\frac{12-11}{11\times12}=\frac{12}{11\times12}-\frac{11}{11\times12}=\frac{1}{11}-\frac{1}{12}\)
\(\frac{1}{38\times39}=\frac{39-38}{38\times39}=\frac{39}{38\times39}-\frac{38}{38\times39}=\frac{1}{38}-\frac{1}{39}\)
\(\frac{1}{39\times40}=\frac{40-39}{39\times40}=\frac{40}{39\times40}-\frac{39}{39\times40}=\frac{1}{39}-\frac{1}{40}\)
\(\Rightarrow B=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+....+\frac{1}{38}-\frac{1}{39}+\frac{1}{39}-\frac{1}{40}\)
\(B=\frac{1}{10}-\frac{1}{40}\)
\(B=\frac{3}{40}\)
ML
26 tháng 6 2017
3.
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}\)
\(A=\frac{99}{100}\)
\(B=\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{38.39}+\frac{1}{39.40}\)
\(B=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{38}-\frac{1}{39}+\frac{1}{39}-\frac{1}{40}\)
\(B=\frac{1}{10}-\frac{1}{40}\)
\(B=\frac{3}{40}\)
HN
12
TM
19 tháng 6 2016
Đặt A=1x2+2x3+3x4+...+2016x2017
=>3A=3x1x2+3x2x3+3x3x4+...+3x2016x2017
=>3A=(3-0)x1x2+(4-1)x2x3+(5-2)x3x4+...+(2018-2015)x2016x2017
=>3A=1x2x3-0x1x2+2x3x4-1x2x3+3x4x5-2x3x4+...+2016x2017x2018-2015x2016x2017
=>3A=2016x2017x2018
=>A=\(\frac{2016\times2017\times2018}{3}\)(tự tính nha)
19 tháng 6 2016
S = 1x2 + 2x3 + 3x4 + 4x5 + ... + 2016x2017
3S = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 2016x2017x(2018-2015)
3S = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 2016x2017x2018 - 2015x2016x2017
3S = 2016x2017x2018
S = 1/3 x 2016x2017x2018.
3 tháng 2 2017
Đặt A = 1.2 + 2.3 + 3.4 + .... + 39.40
3A = 3( 1.2 + 2.3 + 3.4 + .... + 39.40 )
= 1.2.3 + 2.3.3 + 3.4.3 + .... + 39.40.3
= 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 39.40(41 - 38)
= 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ..... + 39.40.41 - 38.39.40
= 39.40.41
\(\Rightarrow A=\frac{39.40.41}{3}=21320\)
17 tháng 6 2015
Gọi biểu thức trên là A, ta có :
A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100
A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3
A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)
A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.
A x 3 = 99x100x101
A = 99x100x101 : 3
A = 333300
đúng cho mik nha !
17 tháng 6 2015
Gọi biểu thức trên là A, ta có :
A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100
A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3
A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)
A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.
A x 3 = 99x100x101
A = 99x100x101 : 3
A = 333300
7 tháng 8 2016
A = 1 x 2 + 2 x 3 + 3 x 4 + ... + 99 x 100
3A = 1 x 2 x (3 - 0) + 2 x 3 x (4 - 1) + 3 x 4 x (5 - 2) + ... + 99 x 100 x (101 - 98)
3A = 1 x 2 x 3 - 0 x 1 x 2 + 2 x 3 x 4 - 1 x 2 x 3 + 3 x 4 x 5 - 2 x 3 x 4 + ... + 99 x 100 x 101 - 98 x 99 x 100
3A = (1 x 2 x 3 + 2 x 3 x 4 + 3 x 4 x 5 + ... + 99 x 100 x 101) - (0 x 1 x 2 + 1 x 2 x 3 + 2 x 3 x 4 + ... + 98 x 99 x 100)
3A = 99 x 100 x 101
A = 33 x 100 x 101
A = 333300
7 tháng 8 2016
A = 1x2+2x3+3x4+4x5+....+99x100
3A=1x2x(3-0)+2x3x(4-1)+3x4x(5-2)+...+99x100x(101-98)
3A= 1x2x3-0x1x2+2x3x4-1x2x3+3x4x5-2x3x4+...+99x100x101-98x99x100
3A= 99x100x101
A=999900 : 3 = 333300
3C = 1x2x3 + 2x3x(4-1) + ... + 11x12x(13-9)
3C = 1x2x3 + 2x3x4 - 1x2x3 + ... + 11x12x13 - 9x11x12
3C = 9x11x12
3C = 1188
C = 396
C = 1x2 + 2x3 + 3x4 + ... + 10x11 + 11x12
=> 3C = 1x2x3 + 2x3x4 - 1x2x3 + ... + 11x12x13 - 9x11x12
=> 3C = 9 x 11 x 12
=> 3C = 1188
=> C = 396