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C=1.2+2.3+...+99.100
3C=1.2.3+2.3.3+...+99.100.3
3C=1.2(3-0)+2.3(4-1)+...+99.100(101-98)
C=99.100.101 phần 3
C=333 300
a)đặt A = 1.2 + 3.4 + 4.5 +...+ 99.100
A=1.2+2.3+3.4+4.5+...+99.100
=>3A=1.2.3+2.3.3+3.4.3+4.5.3+...+99.100.3
=1.2.3+2.3.(4-1)+3.4.(5-2)+4.5.(6-3)+...+99.100.(101-98)
=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+...+99.100.101-98.99.100
=1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-3.4.5+4.5.6-4.5.6+...+99.100.101
=99.100.101=999900
=>A=999900:3=333300
Vậy A=333300
b)D=2 +4 +6 +333 300
D=4+16+36+333 300
D=20+36+333 300
D=56+333 300
D=333 356
a) C = 1.2 + 3.4 + 4.5 +...+ 99.100
\(\Rightarrow\) C = 1.2+2.3+3.4+4.5+...+99.100
\(\Rightarrow\)3C = 1.2.3+2.3.3+3.4.3+4.5.3+...+99.100.3
\(\Rightarrow\)3C = 1.2.3+2.3.(4-1)+3.4.(5-2)+4.5.(6-3)+...+99.100.(101-98)
\(\Rightarrow\)3C = 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+...+99.100.101-98.99.100
\(\Rightarrow\)3C = 1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-3.4.5+4.5.6-4.5.6+...+99.100.101
\(\Rightarrow\)3C = 99.100.101
\(\Rightarrow C=33.100.101\)
\(\Rightarrow C=333300\)
b) D = 2 + 4 + 6 + 333 300
\(\Rightarrow\)D = 4 + 16 + 36 + 333 300
\(\Rightarrow\)D = 20 + 36 + 333 300
\(\Rightarrow\)D = 56 + 333 300
\(\Rightarrow\)D = 333 356
a, C = 1.2 + 2.3 + 3.4 + ... + 99.100
3C = 1.2.3 + 2.3.3 + 3.4.3 + .... + 99.100.3
3C = 1.2.3 + 2.3\((4-1)\)+ 3.4\((5-2)+...\)+ 99.100\((101-98)\)
3C = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100
3C = 99.100.101
C = 99.100.101 :3
C = 333300
Câu b tự làm
P/S : Hoq chắc :>
3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3
= 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + 3.4.5 - ... - 98.99.100 + 99.100.101
= 99.100.101
A=333300
B= (1.2 + 2.3 + 3.4 + ... + 100.101) - (1 + 2 + 3+ 4 + ... + 100)
= 333300 + 10100 - 5050
= 333300 + 5050
= 338350
A = 1*2 + 2*3 + 3*4 + ........+ 99*100
=>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 =1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100
<=> 3A = 99.100.101 = 999900
=> S = 333300
A = \(\frac{5}{1.2}\) + \(\frac{5}{2.3}\) +........+\(\frac{5}{99.100}\)
A = 5.(\(\frac{1}{1.2}\) + \(\frac{1}{2.3}\) +......+\(\frac{1}{99.100}\) )
A = 5. ( \(\frac{1}{1}\) - \(\frac{1}{2}\) +\(\frac{1}{2}-\frac{1}{3}\) +......+\(\frac{1}{99}-\frac{1}{100}\) )
A= 5. (\(1-\frac{1}{100}\))
A= 5.\(\frac{99}{100}\)
A= \(\frac{99}{20}\)
B = \(\frac{1}{2.3}\)+ \(\frac{1}{3.4}\)+............+ \(\frac{1}{9.10}\)
= \(\frac{1}{2}\)- \(\frac{1}{3}\)+\(\frac{1}{3}\)- \(\frac{1}{4}\)+ ...................+\(\frac{1}{9}\)- \(\frac{1}{10}\)
= \(\frac{1}{2}\) - \(\frac{1}{10}\)
= \(\frac{2}{5}\)