tinh B=1.4+2.5+3.6+............+100.103
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Đặt \(A=1.4+2.5+3.6+...+100.103\)
\(=1\left(2.2\right)+2\left(3+2\right)+3\left(4+2\right)+...+100\left(101+2\right)\)
\(=1.2+2.3+3.4+...+100.101+\left(1.2+2.2+3.2+...+100.2\right)\)
\(=1.2+2.3+3.4+...+100.101+2\left(1+2+3+...+100\right)\)
\(=1.2+2.3+3.4+...+100.101+2.100\left(100+1\right):2\)
\(=1.2+2.3+3.4+...+100.101+10100\)
Đặt \(B=1.2+2.3+3.4+...+100.101\)
\(\Rightarrow3B=1.2.3+2.3.3+3.4.3+100.101.3\)
\(\Rightarrow3B=1.2.3+2.3\left(4-1\right)+3.4\left(5-2\right)+...+100.101\left(102-99\right)\)
\(\Rightarrow3B=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+100.101.102-99.100.101\)
\(\Rightarrow3B=100.101.102\)
\(\Rightarrow B=343400\)
Khi đó \(A=343400=10100=333300\)
Đặt A = 1.4 + 2.5 + 3.6 + 4.7 + ... + 100.103
3A = 3.(1.2 + 2.3 + 3.4 + ... + 100.101] + 3.(2 + 4 + 6 + ... + 200)
= 1.2.3 + 2.3.3 + 3.4.3 + ... + 100.101.3 + 3.(2 + 4 + 6 + ... + 200)
\(\Rightarrow\) A = 100.101.105:3 = 353500
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Đặt A = 1.4 + 2.5 + 3.6 + ... + 100.103
= 1.(2 + 2) + 2.(3 + 2) + 3.(4 + 2) +.... + 100.(101 + 2)
= 1.2 + 2.3 + 3.4 + ... + 100.101 + (1.2 + 2.2 + 3.2 + ... + 100.2)
= 1.2 + 2.3 + 3.4 + ... + 100.101 + 2(1 + 2 + 3 + .... + 100)
= 1.2 + 2.3 + 3.4 + .... + 100.101 + 2.100.(100 + 1) : 2
= 1.2 + 2.3 + 3.4 + ... + 100.101 + 10100
Đặt B = 1.2 + 2.3 + 3.4 + .... + 100.101
=> 3B = 1.2.3 + 2.3.3 + 3.4.3 + .... + 100.101.3
=> 3B = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 100.101.(102 - 99)
=> 3B = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + .... + 100.101.102 - 99.100.101
=> 3B = 100.101.102
=> B = 343400
Khi đó A = 343400 - 10100 = 333300
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