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Q=1.2.(3-1)+2.3.(4-1)+3.4.(5-1)+...+19.20.(21-1)=
=(1.2.3+2.3.4+3.4.5+...+19.20.21)-(1.2+2.3+3.4+...+19.20)
Đặt
A=1.2.3+2.3.4+3.4.5+...+19.20.21
4A=1.2.3.4+2.3.4.4+3.4.5.4+...+19.20.21.4=
=1.2.3.4+2.3.4(5-1)+3.4.5.(6-2)+...+19.20.21.(22-18)=
=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-...-18.19.20.21+19.20.21.22=
=19.20.21.22
\(A=\dfrac{19.20.21.22}{4}=5.19.21.22\)
Đặt
B=1.2+2.3+3.4+...+19.20
3B=1.2.3+2.3.3+3.4.3+...+19.20.3=
=1.2.3+2.3.(4-1)+3.4.(5-2)+...+19.20.(21-18)=
=1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-...-18.19.20+19.20.21=
=19.20.21
\(B=\dfrac{19.20.21}{3}=7.19.20\)
Q=A-B
\(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\\ =\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}\\ =\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}\\ =\dfrac{1}{3}-\dfrac{1}{9}\\ =\dfrac{2}{9}\)
Các số nghịch đảo:
\(2\rightarrow\frac{1}{2};6\rightarrow\frac{1}{6};12\rightarrow\frac{1}{12};...;90\rightarrow\frac{1}{90}\)
Gọi A là tổng các số nghịch đảo
\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}\\ =\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{9\cdot10}\\ =1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\\ =1-\frac{1}{10}=\frac{9}{10}\)
B = 1+2-3-4+5+6-7-8+9+10-11-12+..........-299-300+301+302
B = 1+(2-3-4+5)+(6-7-8+9)+.......+(298-299-300+301)+302
B = 1+0+0+....+0+302
B = 1+302
B = 303
2;6;12;20;30;42;56;72;90;110
moi so tu 2 den 6 la 4 don vi moi so tiep theo la cong them 2 don vi nhu 2+4=6;6+6=12....
nhu vay 5 so tiep theo cong them vao 110 la ra : so dau tien la: 22 ;24;26;28;30
vay 5 so do la 110 +22=132 ;132 +24 =156 ;156+26 =182;182+28=210 ;210+30=240
tong cac so :2+6+12+20+30+42+56+72+90+110+132+156+182+210+240=1328
ket qua la 1328
chuc ban hoc gioi nha
neu ban cam thay mh dung thi k cho mk nha cac ban !!!!!!! :))) ^^^
Bài giải
\(B=1\cdot2^2+2\cdot3^2+3\cdot4^2+...+99\cdot100^2\)
\(B=1\cdot2\cdot\left(3-1\right)+2\cdot3\cdot\left(4-1\right)+3\cdot4\cdot\left(5-1\right)+...+99\cdot100\cdot\left(101-1\right)\)
\(B=1\cdot2\cdot3-1\cdot2+2\cdot3\cdot4-2\cdot3+...+99\cdot100\cdot101-99\cdot100\)
\(B=\left(1\cdot2\cdot3+2\cdot3\cdot4+...+99\cdot100\cdot101\right)-\left(1\cdot2+2\cdot3+...+99\cdot100\right)\)
Đặt \(C=1\cdot2\cdot3+2\cdot3\cdot4+...+99\cdot100\cdot101\)
\(4C=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot\left(5-1\right)+...+99\cdot100\cdot101\cdot\left(102-98\right)\)
\(4C=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot5-1\cdot2\cdot3\cdot4+...+99\cdot100\cdot101\cdot102-98\cdot99\cdot100\cdot101\)
\(4C=99\cdot100\cdot101\cdot102\)
\(4C=101989800\)
\(C=101989800\text{ : }4\)
\(C=25497450\)
Bạn vào câu hỏi tương tự tham khảo nha !