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A = 2o + 21 + 22 + ... + 22010
=> 2A = 21 + 22 + 23 + ... + 22010 + 22011
Mà A = 20 + 21 + 22 + ... + 22010
=> 2A - A = A = 1 + 22011
B = 1 + 3 + 32 + ... + 3100
=> 3B = 3 + 32 + 33 + ... + 3100 + 3101
Mà B = 1 + 3 + 32 + ... + 3100
=> 3B - B = 2B = 2 + 3101
=> B = ( 2 + 3101 ) : 2
a) 5 + ( -12 ) - 10
= -7 - 10
= -17
b) 25 - ( -17 ) + 24 - 12
= 25 + 17 + 24 - 12
= 42 + 24 - 12
= 66 - 12
= 54
c) 56 : 54 + 23 . 22 - 225 : 152
= 56 - 4 + 23 + 2 - 32 . 52 : 152
= 52 + 25 - 152 : 152
= 25 + 32 - 1
= 57 - 1
= 56
d) ( -5 - 3 ) . ( 3 - 5 ) : ( -3 + 5 )
= ( -8 ) . ( -2 ) : 2
= -8 . [ ( -2 ) : 2 ]
= -8 . ( -1 )
= 8
a) 5 + ( -12) - 10
= 5 - 12 -10
= -17
b) 25 - ( -17) + 24 - 12
= 25 + 17 + 24 - 12
= 42 + 24 - 12
= ( 42 - 12) + 24
= 30 + 24 = 54
c) 56 : 54 + 23 . 22 - 225 : 152
= 52 + 25 - 1
= 25 + 32 - 1
= 56
d) ( - 5 - 3) . ( 3 - 5) : ( -3 + 5)
= ( -8) . ( -2) : 2
= 16 : 2
= 8
\(3\cdot(x+1)^2=75\)
\(\Leftrightarrow(x+1)^2=75:3=25=5^2\)
\(\Leftrightarrow x+1=5\)
\(\Leftrightarrow x=5-1=4\)
3.(x + 1)2 = 75
=> (x + 1)2 = 75 : 3
=> (x + 1)2 = 25
=> (x + 1)2 = 52
=> \(\orbr{\begin{cases}x+1=5\\x+1=-5\end{cases}}\)
=> \(\orbr{\begin{cases}x=4\\x=-6\end{cases}}\)
1.
A= 5/28 + 5/70 +.....+10/700 = 5/(4.7)+5/(7.10)+....5/(25.28)
3A= 5( 1/4 - 1/7 +1/7-1/10+......+1/25-1/28)
3A= 5 (1/4-1/28)
3A=15/14
A= 5/14
#)Giải :
1. \(A=\frac{10}{54}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
\(A=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(\Rightarrow\frac{3A}{5}=\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\)
\(\Rightarrow\frac{3A}{5}=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\)
\(\Rightarrow\frac{3A}{5}=\frac{1}{4}-\frac{1}{28}=\frac{3}{14}\)
\(\Rightarrow A=\frac{3}{14}\times\frac{5}{3}\)
\(\Rightarrow A=\frac{5}{14}\)
1. C = 1 + 3 + 3^2 + 3^3 + .... + 3 ^11
( 1+ 3 + 3^2 ) +..... + ( 3^9 +3^10+3^11 )
13 . 1 +..... + 3^9 . 13
13 ( 1 +......+ 3^9 ) chia hết cho 13
Câu b tương tự nhé
\(\left(9^{2n}-1\right)⋮10\)
\(9^{2n}-1=81^n-1\)
\(\frac{81^n-1}{10}\inℤ\)
\(81^n-1=......1-1=....0\)
\(\Rightarrowđpcm\)
a) 5.5x.5x + 5 = 56
52x + 6 = 6
2x + 6 = 6
x = 0
b) 8x + 3.8x - 2 = 16 : 2
82x + 1 = 8
2x + 1 = 1
x = 0
c) 7x + 1.7x + 2.7x + 3 = 78 - 3x
73x + 6 = 78 - 3x
3x + 6 = 8 - 3x
x = \(\frac{1}{3}\)