A=1.2.3+3.4.5+5.6.7+...+99.100.101
B=1.2^2+2.3^2+3.4^2+4.5^2+...+99.101^2
Những câu hỏi liên quan
A=1.2.3+3.4.5+5.6.7+...+99.100.101
B=1.2^2+2.3^2+3.4^2+4.5^2+...+99.101^2
Ta có: A = 1.2.3+3.4.5+5.6.7+...+99.100.101
A = 1.3 (5-3) + 3.5 (7-3) + 5.7 (9-3) + ............ + 99.101 (103 - 3)
A = (1.3.5 + 3.5.7 + 5.7.9 + .......... + 99.101.103) - (1.3.3 + 3.5.3 + ....... + 99.101.3)
A = (15+99.101.103.105) : 8 - 3.(1.3 + 3.5 +5.7 + ...... + 99.101)
A = 13517400 - 3.171650
A = 13002450
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Tính:
A=1.2.3+2.3.4+3.4.5+4.5.6+5.6.7+6.7.8+7.8.9+8.9.10
B=1.3.5+3.5.7+5.7.9+7.9.11+......+95.97.99
C=1.2.3+3.4.5+5.6.7+7.8.9+........+98.99.100
D=1.22+2.32+3.42+4.52+....+99.1002
Tính gia trị biểu thức: A=1.2+2.3+3.4+...+99.100; B=12+22+32+...+992+1002; C=1.2.3+2.3.4+3.4.5+4.5.6+5.6.7+6.7.8+7.8.9+8.9.10
c, 4C= (1.2.3+2.3.4+3.4.5+...+8.9.10) .4
==> 4C= [1.2.3.(4-0) + 2.3.4-(5-1) + 8.9.10.(11-7)
==>4C= 1.2.3.4 - 1.2.3.4+ 2.3.4.5-2.3.4.5 + 7.8.9.10- 7.8.9.10 + 8.9.10.11
==> 4C= 8.9.10.11=7920
==> C= 7920 :4=1980
a, Ta có: 3A= 1.2.3+2.3.3+3.4.3+...+99.100.3
3A=1.2.(3-0) + 2.3.(4-1)+ 3.4.(5-2)+ ... + 99.100.( 101-98)
3A=(1.2.3 + 2.3.4+ 3.4.5+ 99.100.101) - (0.1.2 +1.2.3+ 2.3.4 + ... + 98.99.100)
3A= 99.100.101 - 0.1.2
3A= 999900 - 0
3A= 999900
==> A= 999900 : 3
==> A= 333300
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Câu 1 : 1.2+2.3+3.4+...+30.31
Câu 2 : 1.2.3+2.3.4+3.4.5+...+30.31.32
Câu 3 : 1/1.2+1/2.3+1/3.4+...+1/30.31
Câu 4 ; 1/1.3+1/3.5+...+1/99.101
Câu 5 : 1/1.4+1/4.7+...+1/91.94
Câu 6 : 1/1.2.3+1/2.3.4+1/3.4.5+...+1/31.32.33
Câu 7 : 1.1!+2.2!+3.3!+...+10.10!
15 tháng 4 2023 lúc 13:47
a) dfrac{2}{1.2.3}+dfrac{2}{2.3.4}+dfrac{2}{3.4.5}+...+dfrac{2}{18.19.20}b) dfrac{4}{1.3.5}+dfrac{4}{3.5.7}+dfrac{4}{5.7.9}+...+dfrac{4}{21.23.25}c) dfrac{3}{1.2}-dfrac{5}{2.3}+dfrac{7}{3.4}-dfrac{9}{4.5}+...+dfrac{39}{19.20}-dfrac{41}{20.21}d) dfrac{8}{9}cdotdfrac{15}{16}cdotdfrac{24}{25}cdot...cdotdfrac{99}{100}cdotdfrac{120}{121}e) left(1+dfrac{7}{9}right)left(1+dfrac{7}{20}right)left(1+dfrac{7}{33}right)left(1+dfrac{7}{48}right)...left(1+dfrac{7}{180}right)Các bạn không nhất thiết phải làm h...
Đọc tiếp
a) \(\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+\dfrac{2}{3.4.5}+...+\dfrac{2}{18.19.20}\)
b) \(\dfrac{4}{1.3.5}+\dfrac{4}{3.5.7}+\dfrac{4}{5.7.9}+...+\dfrac{4}{21.23.25}\)
c) \(\dfrac{3}{1.2}-\dfrac{5}{2.3}+\dfrac{7}{3.4}-\dfrac{9}{4.5}+...+\dfrac{39}{19.20}-\dfrac{41}{20.21}\)
d) \(\dfrac{8}{9}\cdot\dfrac{15}{16}\cdot\dfrac{24}{25}\cdot...\cdot\dfrac{99}{100}\cdot\dfrac{120}{121}\)
e) \(\left(1+\dfrac{7}{9}\right)\left(1+\dfrac{7}{20}\right)\left(1+\dfrac{7}{33}\right)\left(1+\dfrac{7}{48}\right)...\left(1+\dfrac{7}{180}\right)\)
Các bạn không nhất thiết phải làm hết, làm cho nó dễ hiểu được thì càng tốt để mk vận dụng
a: \(=\dfrac{1}{1\cdot2}-\dfrac{1}{2\cdot3}+\dfrac{1}{2\cdot3}-\dfrac{1}{3\cdot4}+...+\dfrac{1}{18\cdot19}-\dfrac{1}{19\cdot20}\)
=1/2-1/380
=179/380
b: \(=\dfrac{1}{1\cdot3}-\dfrac{1}{3\cdot5}+\dfrac{1}{3\cdot5}-\dfrac{1}{5\cdot7}+...+\dfrac{1}{21\cdot23}-\dfrac{1}{23\cdot25}\)
\(=\dfrac{1}{3}-\dfrac{1}{575}=\dfrac{572}{1725}\)
c: \(=1+\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{19}+\dfrac{1}{20}-\dfrac{1}{20}-\dfrac{1}{21}\)
=1-1/21
=20/21
d: \(=\left(1-\dfrac{1}{9}\right)\left(1-\dfrac{1}{16}\right)\cdot...\cdot\left(1-\dfrac{1}{121}\right)\)
\(=\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{10}{11}\cdot\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{12}{11}\)
\(=\dfrac{2}{11}\cdot\dfrac{12}{2}=\dfrac{12}{11}\)
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1.Tính
A=\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+.....+\dfrac{1}{99.100}\)
B=\(\dfrac{3}{5.6}+\dfrac{3}{6.7}+\dfrac{3}{7.8}+.....+\dfrac{3}{101.102}\)
C=\(\dfrac{1}{1.2.3}+\dfrac{1}{3.4.5}+\dfrac{1}{5.6.7}\)
D=\(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}\)
A=1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100
A=1-1/100 A=99/100 B= (1/5.6+1/6/7+...+1/101.102).3 B=(1/5-1/6+1/6-1/7+...+1/101-1/102).3 B=(1/5-1/102).3 B=97/170
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1) Tính
a) Ta có: \(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{99\cdot100}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(=1-\dfrac{1}{100}=\dfrac{99}{100}\)
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tính giá trị biểu thức :
A=\(1.2+2.3+3.4+...+99.100\)
B=\(1^2+2^2+3^2+...+99^2+100^2\)
C=\(1.2.3+2.3.4+3.4.5+4.5.6+5.6.7+6.7.8+7.8.9+8.9.10\)
\(A=1\cdot2+2\cdot3+3\cdot4+...+99\cdot100\)
\(3A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+...+99\cdot100\cdot\left(101-98\right)\)
\(3A=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+...+99\cdot100\cdot101-98\cdot99\cdot100\)
\(3A=99\cdot100\cdot101\Rightarrow A=\dfrac{99\cdot100\cdot101}{3}=333300\)
\(B=1^2+2^2+3^2+...+99^2+100^2\)
\(=\dfrac{100\cdot\left(100+1\right)\cdot\left(2\cdot100+1\right)}{6}\)
\(=\dfrac{2030100}{6}=338350\)
\(C=1\cdot2\cdot3+2\cdot3\cdot4+...+8\cdot9\cdot10\)
\(4C=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot\left(5-1\right)+...+8\cdot9\cdot10\cdot\left(11-7\right)\)
\(4C=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot5-1\cdot2\cdot3\cdot4+...+8\cdot9\cdot10\cdot11-7\cdot8\cdot9\cdot10\)
\(4C=8\cdot9\cdot10\cdot11\Rightarrow C=\dfrac{8\cdot9\cdot10\cdot11}{4}=1980\)
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A = 1 . 2 + 2 . 3 + 3 . 4 + 99 . 100
3A = 1 . 2 . 3 + 2 . 3 . (4 - 1) + 3 . 4 . (5 - 2) + ... + 99 . 100 . (101 - 98)
3A = 1 . 2 . 3 + 2 . 3 . 4 - 2 . 3 . 1 + 3 . 4 . 5 - 3 . 4 . 2 + ... + 99 . 100 . 101 - 99 . 100 . 98
3A = 99 . 100 . 98
A = 33 . 100 . 98
A = 323400
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Bài 1:Tính tổng
A=1.2+3.4+5.6+...+99.100
Bài 2:Tính tổng
A=1.2.3+3.4.5+5.6.7+...+98.99.100
Bài 1:Tính tổng
A=1.2+3.4+5.6+...+99.100
Bài 2:Tính tổng
A=1.2.3+3.4.5+5.6.7+...+98.99.100