cho A=1+4+4^2+4^3+4^4+......+4^59
giúp mk nha
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\(\frac{1}{2}\div\frac{3}{4}+\frac{1}{6}\div\frac{3}{4}\)
\(=\frac{3}{4}\div\left(\frac{1}{2}+\frac{1}{6}\right)\)
\(=\frac{3}{4}\div\frac{2}{3}\)
\(=\frac{9}{8}\)
\(\frac{1}{2}\div\frac{3}{4}-\frac{1}{6}\div\frac{3}{4}\)
\(=\left(\frac{1}{2}-\frac{1}{6}\right)\div\frac{3}{4}\)
\(=\frac{1}{3}\div\frac{3}{4}\)\
\(=\frac{4}{9}\)
1/2 : 3/4 + 1/6 : 3/4 = 1/2 x 4/3 + 1/6 x 4/3 = 4/3 x (1/2 + 1/6) = 4/3 x 2/3 = 8/9
1/2 : 3/4 - 1/6 : 3/4 = 1/2 x 4/3 - 1/6 x 4/3 = 4/3 x (1/2 - 1/6) = 4/3 x 1/3 = 4/9
1+3-2+5-7+4-2-7+5+6-4+7-1+2
= 10
cậu nhé !!!
k mình nha !!!
a) \(A=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{31.34}\)
\(A=\frac{2}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{31}-\frac{1}{34}\right)\)
\(A=\frac{2}{3}.\left(1-\frac{1}{34}\right)\)
\(A=\frac{2}{3}\cdot\frac{33}{34}=\frac{11}{17}\)
b) \(B=\frac{3}{1}+\frac{3}{3}+\frac{3}{6}+...+\frac{3}{210}\)
\(B=\frac{6}{2}+\frac{6}{6}+\frac{6}{12}+...+\frac{6}{420}\) ( 3/1 = 6/2; 6/6=3/3;..)
\(B=\frac{6}{1.2}+\frac{6}{2.3}+\frac{6}{3.4}+...+\frac{6}{20.21}\)
\(B=6.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{20}-\frac{1}{21}\right)\)
\(B=6.\left(1-\frac{1}{21}\right)=6\cdot\frac{20}{21}=\frac{40}{7}\)
\(A = 1 + 4 + 4^2 + ... + 4\)\(20\)
\(4A = 4 + 4^2 + 4^3 + ...+ 4\)\(21\)
\(4A - A = ( 4+ 4^2 + 4^3 + ... + 4\)\(21\)\()\)\(- ( 1 + 4 + 4^2 + ... + 4\)\(20\) \()\)
\(3A = 2\)\(21\) \(- 1\)
\(\Leftrightarrow\)\(3A + 1 = 2\)\(21\)\(= ( 2^3)^7\)\(= 8^7\)
\(Ta có : 8^7 < 63^7 \)
\(Nên 3A + 1 < 63^7\)
Vì A= 4^0 + 4^1 + 4^2+ 4^3+....+4^20
Suy ra: 4A= 4^1+4^2+4^3+4^4+......+ 4^21
Suy ra:4A-A= 4^21 - 4^0
Suy ra: 3A = 4^21-1
Suy ra: A= (4^21-1) : 3
Suy ra: 3A+1= 3. [ ( 4^21-1) : 3] +1
Suy ra: 3A+1 = ( 4^21-1)+1
Suy ra: 3A + 1 = 4^21= (4^3)^7=64^7
Vì 64 > 63; 7=7
Suy ra: 64^7 > 63^7 hay 3A+1 > 63^7
Ta có: 4;42;43;...;429;430 chia hết cho 4
Nên 4+42+43+...+429+430 chia hết cho 4
Nên A=1+4+42+...+429+430 không chia hết cho 4( vì 1 không chia hết cho 4)
Vậy A không chia hết cho 4
A=(4^60-1):3