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\(B=\left(\frac{1}{4}-1\right)\cdot\left(\frac{1}{9}-1\right).....\left(\frac{1}{81}-1\right)\cdot\left(\frac{1}{100}-1\right)\)
\(B=\frac{-3}{4}\cdot\frac{-8}{9}....\frac{-80}{81}\cdot\frac{-99}{100}\)
\(B=-\left(\frac{3}{4}\cdot\frac{8}{9}\cdot\cdot\cdot\cdot\frac{99}{100}\right)\)
\(B=-\left(\frac{3\cdot8\cdot15\cdot24\cdot....\cdot63\cdot80\cdot99}{2^2\cdot3^2\cdot4^2\cdot\cdot\cdot\cdot\cdot9^2\cdot10^2}\right)\)
\(B=-\left(\frac{1\cdot3\cdot2\cdot4\cdot3\cdot5\cdot\cdot\cdot\cdot8\cdot10\cdot9\cdot11}{2^2\cdot3^2\cdot4^2\cdot\cdot\cdot\cdot9^2\cdot10^2}\right)\)
\(B=-\frac{11}{2\cdot10}\)
\(B=\frac{-11}{20}\)
\(B=\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right)...\left(\frac{1}{100}-1\right)\)
\(B=\frac{-3}{2^2}.\frac{-8}{3^2}...\frac{-99}{10^2}\)
\(B=-\left(\frac{3}{2^2}.\frac{8}{3^2}...\frac{99}{10^2}\right)\)(có 9 thừa số, mỗi thừa số là âm nên kết quả là âm)
\(B=-\left(\frac{1.3}{2.2}.\frac{2.4}{3.3}...\frac{9.11}{10.10}\right)\)
\(B=-\left(\frac{1.2...9}{2.3...10}.\frac{3.4...11}{2.3...10}\right)\)
\(B=-\left(\frac{1}{10}.\frac{11}{2}\right)\)
\(B=-\frac{11}{20}\)
A=1.1+2.2+3.3+...+99.99+100.100
3A=1.2.3+2.3.(4-1)+...99.100.(101-98)
3A=1.2.3+2.3.4-1.2.3+...+99.100.101-98.99.100
3A=99.100.101=999900
A= 999900:3=333300
\(A=1^2+2^2+3^2+...+100^2\)
\(\Rightarrow A=1\left(2-1\right)+2\left(3-1\right)+3\left(4-1\right)+...+100\left(101-1\right)\)
\(\Rightarrow A=1.2-1+2.3-2+3.4-3+...+100.101-100\)
\(\Rightarrow A=1.2+2.3+...+100.101-\left(1+2+3+...+100\right)\)
\(\Rightarrow A=\frac{100.101.102}{3}-\frac{\left(100+1\right)\left[\left(100-1\right):1+1\right]}{2}=\frac{100.101.102.2}{6}-\frac{101.100.3}{6}\)
\(\Rightarrow A=\frac{100.101\left(102.2-3\right)}{6}\)
\(4^{2017}:\left(4^{2014}+3\cdot4^{2014}\right)\)
\(=4^{2017}:4^{2014}\left(1+3\right)\)
\(=4^3\cdot4\)
\(=4^4\)
\(=256\)
Bài làm
C = 1 . 2 . 3 + 2 . 3 . 4 + 4 . 5 . 6 + ..... + 48 . 49 . 50
4C = 1 . 2 . 3 . 4 + 2 . 3 . 4 . ( 5 - 1 ) + ..... + 48 . 49 . 50 . ( 51 - 47 )
4C = 1 . 2 . 3 . 4 + 2 . 3 . 4 . 5 − 1 . 2 . 3 . 4 + ..... + 48 . 49 . 50 . 51 − 47 . 48 . 49 . 50
4C = 48 . 49 . 50 . 51
\(\Rightarrow C=\frac{5997600}{4}=1499400\)
Vậy C = 1499400
# Học tốt #
1/(-37) +14+26+37
=[(-37)+37] +(14+26)
= 0 + 40
= 40
2/(-24) +6 +10+24
=[(-24)+24] +(10+6)
= 0 +16
=16
3/15+23+9+(-25) +9+(-23)
=[(-23)+23] +[(-25)+15] +(9+9)
= 0 + (-10) +18
= 0 + 8
= 8
4/60 +33 +(-50) +(-33)
=[(-33)+33]+[60 +(-50)]
= 0 + 10
= 10
5/(-16)+ (-209) + (-14) +209
=[(-209)+209] +[(-16)+(-14)]
= 0 +(-30)
= -30
6/(-12) +(-13)+36 +(-11)
=[(-12) +(-11)] +[ 36+(-13)]
= (-23) + 23
= 0
Chúc bn hok tốt !!!
1, (-37)+14+26+37=[(-37)+37]+14+26=0+40=40
2, (-24)+6+10+24=[(-24)+24]+6+10=0+16=16
3 , 15+23+(-25)+(-23)=[15+(-25)]+[23+(-23)]=-10
4, 60+33+(-50)+(-33)= [60+(-50)]+[33+(-33)]=10
5, (-16)+(-209)+(-14)+209=[(-16)+(-14)]+[(-209)+209]=-30
6, (-12)+(-13)+36+(-11)=[(-12)+(-11)]+[(-13)+36]=(-23)+23=0