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A= 1+(2-3)+(5-4)+...+(98-99)-100
=1-1+1-1+...+1-1-100
=-100
Ta có: C=1 - 2 - 3 - 4 + 5 - 6 - 7 - 8 + 9 - 10 - 11 - 12 +... + 97 - 98 - 99 - 100
C= ( 1 - 2 - 3 - 4 ) + ( 5 - 6 - 7 - 8 ) + ( 9 - 10 - 11 - 12 ) + ... + ( 97 - 98 - 99 - 100 )
C= - 8 + - 16 + -24 + ... + -200
C= - ( 8 + 16 + 24 +... + 200 )
C= - \(\frac{\left(8+200\right).25}{2}\)= - 2600
nhớ ấn đúng cho mình nhé!
a/ A= 1-3+5-7+9-11+......+97-99
= -2+(-2)+(-2)+......+(-2)
= (-2).25=-50
b/B=-1-2-3-4-...-100
=-(1+2+3+4+...+100)
=-5050
c/C=1-2+3-4+5-6+......+99-100
= -1+(-1)+(-1)+.............+(-1)
=(-1).50=-50
d/D=1-2-3+4+5-6-7+8+9-....+94-95
= (1-2-3+4)+(5-6-7+8)+.......+(92-93-94+95)
= 0+0+0+...+0=0
B = \(\frac{9}{1.2}-\frac{9}{2.3}-...-\frac{9}{99.100}\)
B = \(\frac{9}{2}-\left(\frac{9}{2.3}+\frac{9}{3.4}+...+\frac{9}{99.100}\right)\)
B = \(\frac{9}{2}-9.\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)
B = \(\frac{9}{2}-9.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)
B = \(\frac{9}{2}-9.\left(\frac{1}{2}-\frac{1}{100}\right)\)
B = \(\frac{9}{2}-9.\frac{49}{100}\)
B = \(\frac{9}{2}-\frac{441}{100}=\frac{9}{100}\)
\(B=\frac{9}{1\cdot2}-\frac{9}{2\cdot3}-.....-\frac{9}{99\cdot100}\)
\(=\frac{9}{2}-9\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+....+\frac{1}{99\cdot100}\right)\)
\(=\frac{9}{2}-9\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{99}-\frac{1}{100}\right)\)
\(=\frac{9}{2}-9\left(1-\frac{1}{100}\right)\)
\(=\frac{9}{2}-\frac{891}{100}\)
tự tính nốt.
\(B=\frac{9}{1.2}-\frac{9}{2.3}-.....-\frac{9}{99.100}\)
\(B=\frac{9}{1.2}+\frac{-9}{2.3}+\frac{-9}{3.4}+....+\frac{-9}{99.100}\)
\(B=\frac{9}{2}+\left(-9\right)\left(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{99.100}\right)\)
\(B=\frac{9}{2}+\left(-9\right).\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}\right)\)
\(B=\frac{9}{2}+\left(-9\right).\left(1-\frac{1}{100}\right)\)
\(B=\frac{9}{2}+\left(-9\right).\frac{99}{100}\)
\(B=\frac{9}{2}+\frac{-891}{100}\)
\(B=\frac{450}{100}+\frac{-891}{100}\)
\(B=\frac{-441}{100}\)
\(\frac{9}{1.2}+\frac{9}{2.3}+\frac{9}{3.4}+...+\frac{9}{99.100}\)
=\(9.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)
=\(9.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)
=\(9.\left(\frac{1}{1}-\frac{1}{100}\right)\)
=\(9.\frac{99}{100}\)
=\(\frac{891}{100}\)