Tính tổng: 1x2 + 2x3 + 3x4 + 4x5 +.............+ 99x100
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HV
0
YN
1
28 tháng 12 2016
Tính tổng:
1x2 + 2x3 + 3x4 + 4x5 +.............+ 99x100
Giải
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
PT
1
CM
10 tháng 11 2017
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 = 99x100x101 A = 333300
PT
1
CM
2 tháng 3 2018
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 = 99x100x101
A = 333300
HT
1
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
17 tháng 6 2023
1 \(\times\) 2 \(\times\) 3 = 1 \(\times\) 2 \(\times\) 3
2 \(\times\) 3 \(\times\) 3 = 2 \(\times\) 3 \(\times\) ( 4 -1) = 2 \(\times\) 3 \(\times\) 4 - 1 \(\times\) 2 \(\times\) 3
3 \(\times\) 4 \(\times\) 3 = 3 \(\times\) 4 \(\times\) ( 5 -2) = 3 \(\times\) 4 \(\times\) 5 - 2 \(\times\) 3 \(\times\) 4
4 \(\times\) 5 \(\times\) 3 = 4 \(\times\) 5 \(\times\) ( 6- 3) = 4 \(\times\) 5 \(\times\) 6 - 3 \(\times\) 4 \(\times\) 5
..................................................................................
99\(\times\)100\(\times\)3 = 99\(\times\)100\(\times\)(101-98) =99\(\times\)100\(\times\)101 - 98\(\times\)99\(\times\)100
Cộng vế với vế ta được:
1\(\times\)2\(\times\)3 + 2\(\times\)3\(\times\)3 + 3\(\times\)4\(\times\)3+ ...+99\(\times\)100\(\times\)3 = 99\(\times\)100\(\times\)101
(1\(\times\)2 + 2\(\times\)3 + 3\(\times\)4 +...+99\(\times\)100)\(\times\)3 = 99\(\times\)100\(\times\)101
1\(\times\)2 + 2\(\times\)3 + 3\(\times\)4+...+99\(\times\)100 = (99 \(\times\)100 \(\times\)101):3
1\(\times\)2 + 2\(\times\)3 + 3\(\times\)4+...+99\(\times\)100 = 333 300
20 tháng 3 2019
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
hok tốt
ZV
2
17 tháng 6 2016
A=1x2+2x3+3x4+4x5+......+99x100+100x101
3A=1x2x(3-0)+2x3x(4-1)+3x4x(5-2)+4x5x(6-3)+...+99x100x(101-98)+100x101x(102-99)
3A=1x2x3-0x1x2+2x3x4-1x2x3+3x4x5-2x3x4+4x5x6-3x4x5+...+99x100x101-98x99x100+100x101x102-99x100x101
3A=(1x2x3+2x3x4+3x4x5+4x5x6+...+99x100x101+100x101x102)-(0x1x2+1x2x3+2x3x4+3x4x5+...+98x99x100+99x100x101)
3A=100x101x102
A=100x101x102:3
A=343400
17 tháng 6 2016
A = 1x2 + 2x3 + 3x4 + 4x5 + ... + 99x100 + 100x101
3A = 1x2x(3-0) + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98) + 100x101x(102-99)
3A = 1x2x3 - 0x1x2 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100 + 100x101x102 - 99x100x101
3A = 100x101x102 - 0x1x2
3A = 100x101x102
A = 100x101x34
A = 343400
PM
2
11 tháng 9 2015
A = 1 x 2 + 2 x 3 + ....... + 10 x 11
3A = 1 x 2 x 3 + 2 x 3 x 3 + ..........+ 10 x 11 x 3
3A = 1 x 2 x (3-0) + 2 x 3 x (4-1) + .......... + 10 x 11 x (12 -9)
3A = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + ........... + 10 x 11 x 12 - 9 x 10 x 11
3A = (1 x 2 x 3 - 1 x 2 x 3) + ( 2 x 3 x 4 - 2 x 3 x 4) +............ + 10 x 11 x 12
3A = 10 x 11 x 12 = 1320
A = 1320 : 3 = 440
V
7 tháng 7 2019
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
=>3D =1.2.3 + 2.3.3 + 3.4.3 + ..... + 99.100 .3
=> 3D = 1.2.3 - 2.3. ( 4-1) + 3.4. (5-2) + ... + 98.99 (100 - 97 ) + 99 . 100 . ( 101-98)
=> 3D= 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 +... + 98.99.100 -97.98.99 +99.100.101-98.99.100
=> 3D= 99.100.101
=> 3D= 999 900
D= 999 900 .3 = 333 300
=>3D =1.2.3 + 2.3.3 + 3.4.3 + ..... + 99.100 .3
=> 3D = 1.2.3 - 2.3. ( 4-1) + 3.4. (5-2) + ... + 98.99 (100 - 97 ) + 99 . 100 . ( 101-98)
=> 3D= 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 +... + 98.99.100 -97.98.99 +99.100.101-98.99.100
=> 3D= 99.100.101
=> 3D= 999 900
D= 999 900 .3 = 333 300