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\(P=\left(1^2+2^2+...............+2015^2\right):\left(2^2+4^2+........+4030^2\right)\)
\(P=\left(1^2+2^2+............+2015^2\right):\left[\left(1.2\right)^2+\left(2.2\right)^2+.............+\left(2.2015\right)^2\right]\)
\(P=\left(1^2+2^2+........+2015^2\right):\left(1^2.2^2+2^2.2^2+...............+2015^2.2^2\right)\)
\(P=\left(1^2+2^2+......+2015^2\right):2^2.\left(1^2+2^2+.........+2015^2\right)\)
\(P=\left(1^2+2^2+........+2015^2\right).\frac{1}{2^2.\left(1^2+2^2+..............+2015^2\right)}\)
\(P=\frac{1^2+2^2+...............+2015^2}{2^2.\left(1^2+2^2+............+2015^2\right)}=\frac{1}{2^2}=\frac{1}{4}\)
Chúc bạn học tốt
Ta có: \(M=\left(4^{10}+4^{11}\right)+\left(4^{12}+4^{13}\right)+...+\left(4^{198}+4^{199}\right)\)
\(=4^{10}.\left(1+4\right)+4^{12}.\left(1+4\right)+...+4^{198}.\left(1+4\right)\)
\(=4^{10}.5+4^{12}.5+...+4^{198}.5\)
\(=5.\left(4^{10}+4^{12}+...+4^{198}\right)\text{chia hết cho 5}\)
=> M chia hết cho 5
=> M là B(5) => đpcm.
- Bài 1:
\(A=\frac{2^{10}.13+2^{10}.65}{2^8.104}=\frac{2^{10}.13+2^{10}.13.5}{2^8.2^2.13.2}\)
\(=\frac{2^{10}.13\left(1+5\right)}{2^{10}.13.2}=\frac{2^{10}.13.6}{2^{10}.13.2}=\frac{6}{2}=3\)
\(B=\left(1+2+3+...+100\right)\left(1^2+2^2+3^2+...+100^2\right)\left(65.111-13.15.37\right)\)
\(=\left(1+2+3+...+100\right)\left(1^2+2^2+...+100^2\right)\left(65.111-13.5.3.37\right)\)
\(=\left(1+2+...+100\right)\left(1^2+2^2+...+100^2\right)\left(65.111-65.111\right)\)
\(=\left(1+2+...+100\right)\left(1^2+2^2+...+100^2\right).0\)
\(=0\)
- Bài 2:
\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=5750\)
\(x+1+x+2+x+3+...+x+100=5750\)
\(x+x+x+...+x+1+2+3+...+100=5750\)
\(100x+5050=5750\)
\(100x=5750-5050\)
\(100x=700\)
\(x=700:100\)
\(x=7\)
t_i_c_k cho mình nha ^^
a ) ( - 14 ) + 12 + ( - 12 ) . ( 23 - 7 )
= - 2 + ( - 12 ) . ( 8 - 7 )
= - 2 + ( - 12 ) . 1
= - 2 + ( - 12 )
= - 14
a) x2015 = x
=> x 2015 - x = 0
x.(x2014-1) = 0
=> x = 0 => x2014 - 1 = 0
x2014 = 1
=> x = 1 hoặc x = -1
KL:...
b) 3x+3x+1+3x+2 = 1053
3x+3x.3 + 3x.32 = 1053
3x.( 1 + 3 + 32) = 1053
3x. 13 = 1053
3x = 81 = 34
=> x = 4
3x + 3x+1 + 3x+2 = 1053
3x(1 + 3 + 32) = 1053
3x. 13 = 1053
3x = 1053 : 13 = 81
x =4
\(2015^2.\left(x-10\right)=2015^6\)
\(\Rightarrow x-10=2015^6:2015^2\)
\(\Rightarrow x-10=2015^4\)
Từ đây tự tính tiếp nhé em!
20155 × ( x - 10 ) = 20156
( x - 10 ) = 20156 ÷ 20155
x - 10 = 2015
x = 2015 + 10
x = 2025
Chúc bạn học tốt nha!