Đặt A = 1.2 + 2.3 + 3.4 + ..... + 48.49 + 49.50
=> 3A = 1.2.(3 - 0) + 2.3.(4 - 1) + 3.4.(5 - 2) + ..... + 48.49.(50 - 47) + 49.50.(51 - 48)
=> 3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ..... + 49 .50,51
=> 3A = 48.50.51
=> A =48.50.51 / 3
=> A = 41650
Tính
a) \(\dfrac{13}{50}.\left(-15.5\right):\dfrac{13}{50}.84\dfrac{1}{2}\)
b) \(\dfrac{\left(-0,7\right)^2.\left(-5\right)^3}{\left(-2\dfrac{1}{3}\right)^3.\left(1\dfrac{1}{2}\right)^4.\left(-1\right)^5}\)
Thực hiện phép tính:
a) 49.\(\left(\frac{7}{2}\right)^{-2}\).\(\left(2^2\right)^{-1}\)
b)\(\left[\left(\frac{4}{3}\right)^{-3}.\left(\frac{3}{4}\right)^{-2}\right]\):\(\left(-\frac{2}{3}\right)^{-2}\)
c \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{50.51}\)( Có 50 số hạng)
d)0,(6)+0,8(3)-0,75
Tính :
\(A=\left(1000-1^3\right).\left(1000-2^3\right).\left(1000-3^3\right).........\left(1000-50^3\right)\)
tính
a,\(\sqrt{49}-\sqrt{\left(-5\right)^2}-5\sqrt{1,44}+3\sqrt{\frac{4}{9}}\)
b, \(\left(2\sqrt{3}\right)^2-\left(3\sqrt{2}\right)^2+\left(4.\sqrt{0,5}\right)^2-\left(\frac{1}{5}\sqrt{125}\right)^3\)
c, \(\left(2^{-1}+3^{-1}\right).\left(2^{-1}-2^{-1}\right).\left(2^{-1}.2^0\right)^{-4}:2^3\)
\(3\frac{1}{2}.\frac{4}{49}-\left[2,\left(4\right).2\frac{5}{11}\right]:\left(\frac{-42}{8}\right)\)
\(\left[0,\left(5\right).0,\left(2\right)\right]:\left(3\frac{1}{3}:\frac{33}{25}\right)-\left(\frac{2}{5}.3\frac{1}{3}\right);\frac{4}{3}\)
Tính
\(Tính:\left(1000-1^3\right).\left(1000-2^3\right).\left(1000-3^3\right)...\left(1000-50^3\right)\)
Tính a):\(\frac{\left(\frac{4}{9}\right)^2.\left(-\frac{9}{16}\right).\left(-1\right)^{19}}{\left(\frac{4}{25}\right)^2.\left(-\frac{25}{144}\right)^2.\left(-\frac{49}{144}\right)^2}\)
b)\(\frac{\left(\frac{2}{3}\right)^3.\left(-\frac{3}{4}\right)^2.\left(-1\right)^{2003}}{\left(\frac{2}{5}\right)^2.\left(-\frac{5}{12}\right)^3}\)
Bài 1 : Tính
\(a,\left(\frac{1^{ }}{2}\right)^{15}\cdot\left(\frac{1}{4}\right)^{20}\)
b, \(\left(\frac{1}{9}\right)^{25}:\left(\frac{1}{3}\right)^{30}\)
Bài 2 : Chứng minh rằng 7^6 + 7^5 - 7^4 chia hết cho 55
Tính A = 1+5+5^2 + 5^3 +...+5^49+5^50
bÀI 3
a, tìm giá trị lớn nhất của biểu thức :
\(A=\frac{3}{\left(X+2\right)^2+4}\)
B, tÌM GIÁ trị nhỏ nhất :
\(B=\left(x+1\right)^2+\left(y+3\right)^2+1\)
Bài 4 : Chứng minh rằng góc tạo bỏi 2 tia phân giác của 2 góc kề bù là góc vuông
Tính
a) \(\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6\)
b) \(\left(-\frac{1}{3}\right)^{-1}-\left(-\frac{6}{7}\right)^0+\left(\frac{1}{2}\right):2\)
