1x3+2x4+...+97x100=?
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a) 5/1x3 + 5/3x5 + 5/5x7 + ........ + 5/43x45
b) 6/1x4 + 6/4x7 + 6/7x10 + ...... + 6/97x100
1
DN
21 tháng 8 2015
\(a,\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{43.45}=\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{43.45}\right)=\frac{5}{3}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{43}-\frac{1}{45}\right)=\frac{5}{3}.\frac{44}{45}=\frac{44}{27}\)
12 tháng 3 2022
=1(2+1)+2(3+1)+3(4+1)+...+100(101+1)
=1.2+1+2.3+2+3.4+3+...+100.101+100
=(1.2+2.3+3.4+..+100.101)+(1+2+3+...+100)
=333300+5000
=338300
2 tháng 7 2018
\(S=1.3+2.4+3.5+...+99.101\)
\(\Rightarrow S=1\left(2+1\right)+2\left(3+1\right)+...+99\left(100+1\right)\)
\(\Rightarrow S=\left(1.2+2.3+...+99.100\right)+\left(1+2+3+...+99\right)\)
Đặt \(A=1.2+2.3+...+99.100\)
\(\Rightarrow3A=1.2.3+2.3.\left(4-1\right)+...+99.100.\left(101-98\right)\)
\(\Rightarrow3S=1.2.3+2.3.4-1.2.3+...+99.100.101-98.99.100\)
\(\Rightarrow S=\frac{99.100.101}{3}\)
Đặt \(B=1+2+3+...+99\)
\(\Rightarrow B=\frac{\left(99+1\right)\left[\left(99-1\right):2+1\right]}{2}\)
\(\Rightarrow B=\frac{100.50}{2}=2500\)
\(\Rightarrow S=A+B=\frac{99.100.101}{3}+2500\)
2 tháng 7 2018
S = 1 x 3 + 2 x 4 + 3 x 5 + ... + 99 x 101
S = ( 1 x 3 + 3 x 5 + ...+ 99 x 101) + ( 2 x 4 + ...+ 98 x 100)
Đặt A = 1 x 3 + 3 x 5 + ...+ 99 x 101
=> 6 A = 1 x 3 x 6 + 3 x 5 x 6 + ...+ 99 x 101 x 6
6 A = 1 x 3 x ( 5+1) + 3 x 5 x ( 7-1) + ...+ 99 x 101 x ( 103 - 97)
6A = 1 x 3 x 5 + 1 x 3 + 3 x 5 x 7 - 1 x 3 x 5 + ...+ 99 x 101 x 103 - 97 x 99 x 101
6A = ( 1 x 3 + 1 x 3 x 5 + 3 x 5 x 7 +...+ 99 x 101 x 103) - ( 1 x 3 x 5 + ...+ 97 x 99 x 101)
6A = 1 x 3 + 99 x 101 x 103
\(\Rightarrow A=\frac{1.3+99.101.103}{6}=171650\)
Đặt B = 2 x 4 + ...+ 98 x 100
=> 6B = 2 x 4 x 6 + 4 x 6 x 6 + ...+ 98 x 100 x 6
6B = 2 x 4 x 6 + 4 x 6 x ( 8-2) + ...+ 98 x 100 x ( 102 - 96)
6B = 2 x 4 x 6 + 4 x6 x8 - 2x4x6 + ...+ 98x100x102 - 96x98x100
6B = ( 2 x 4 x 6 + 4 x 6 x 8 +...+98x100x102) - ( 2x4x6+...+96x98x100)
6B = 98 x 100 x 102
\(\Rightarrow B=\frac{98.100.102}{6}=166600\)
Thay A;B vào S, có
S = 171 650 + 166 600
S = 338 250
14 tháng 8 2015
có C= 1x3+2x4+3x5+...+18x20
C= 1x(1+2)+2x(1+3)+3x(1+4)+....+18x(1+19)
C= 1x1+1x2+1x2+2x3+1x3+3x4+....+1x18+18x19
C= 1+1x2+2+2x3+3+3x4+....+18+18x19
C= (1+2+3+4+...+18) + (1x2+2x3+3x4+....+18x19)
C= 171+ (1x2+2x3+....+18x19)
Đặt A=1x2+2x3+3x4+...+18x19
3A=1x2x3+2x3x3+3x4x3+....+18x19x3
3A=1x2x(3-0)+2x3x(4-1)+3x4x(5-2)+.....+18x19x(20-17)
3A= 1x2x3-0+2x3x4-1x2x3+3x4x5-2x3x4+.....+18x19x20-17x18x19
3A= 18x19x20
3A= 6840
A=2280
Vậy C= 171+2280=2451
S
0
A=1x3+2x4+3x5+...+99x100
A=(1x3+3x5+...+99x101)+(2x4+4x6+...+98x100)
đặt S=1x3+3x5+...+99x101
=>6S=6x(1x3+3x5+...+99x101)
=1x3x(5+1)+3x5x(7-1)+...+97x99x(101-95)+99x101x(103-97)
=1x3x5+1x3x1+3x5x7-1x3x5+....+97x99x101-95x97x99+99x101x103-97x99x101
=1x3x1+99x101x103
=>S=(3+99x101x103):6=171650
=>C=171650+(2x4+4x6+...+98x100)
đặt A=2x4+4x6+...+98x100
=>6A=6x(2x4+4x6+...+98x100)
=>6A=2x4x6+4x6x(8-2)+...+96x98x(100-94)+98x100x(102-96)
=2x4x6+4x6x8-2x4x6+...+96x98x100-94x96x98+98x100x102-96x98x100
=98x100x102
=>A=98x100x102:6=166600
=>A=166600+171650
=>A=338250