\(A=1+\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+...+\dfrac{1}{12}\left(1+2+3+...+12\right)\)\(A=1+\dfrac{2+1}{2}+\dfrac{3+1}{2}+...+\dfrac{12+1}{2}\)
\(A=1+\dfrac{1}{2}\left(3+4+5+...+13\right)\)
\(A=1+\dfrac{1}{2}\left(1+2+3+...+13\right)-\dfrac{3}{2}\)
\(A=1+\dfrac{1}{2}.\dfrac{13\left(13+1\right)}{2}-\dfrac{3}{2}\)
\(A=1+\dfrac{91}{2}-\dfrac{3}{2}=45\)
tính :
a, \(\left[6.\left(-\dfrac{1}{3}\right)^2-3.\left(-\dfrac{1}{3}\right)+1\right]:\left(-\dfrac{1}{3}-1\right)\)
b, \(\dfrac{\left(\dfrac{2}{3}\right)^3.\left(-\dfrac{3}{4}\right)^2.\left(-1\right)^{2003}}{\left(\dfrac{2}{5}\right)^2.\left(-\dfrac{5}{12}\right)^3}\)
Bài 1: Thực hiện phép tính:
\(\sqrt{25}\)x\(\left(0,4-1\dfrac{1}{12}\right)\):\(\left[\left(-2\right)^3x\dfrac{11}{8}\right]\)
1. thực hiện phép tính
a. \(-1\dfrac{1}{2}.21\dfrac{1}{3}+1\dfrac{1}{2}.1\dfrac{1}{3}\)
b. \(-3^2-\left(\dfrac{1}{2}\right)^{-2}:2^2+\left(\dfrac{2}{3}\right)^0:\left(\dfrac{3}{4}\right)^{-1}\)
c. \(\sqrt{12}+\sqrt{27}-\sqrt{3}\)
\(\dfrac{\left(13\dfrac{1}{4}-2\dfrac{5}{27}-10\dfrac{5}{6}\right).230\dfrac{1}{25}+46\dfrac{3}{4}}{\left(1\dfrac{3}{10}+\dfrac{10}{3}\right):\left(12\dfrac{1}{3}-14\dfrac{2}{7}\right)}\)
\(\dfrac{\left(1+2+3+...+99+100\right)\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{9}\right)\left(63.1,2-21.3,6\right)}{1-2+3-4+.....+99-100}\)
Thực hiện tính
M=\(1+\dfrac{1}{2}\cdot\left(1+2\right)+\dfrac{1}{3}\cdot\left(1+2+3\right)+\dfrac{1}{4}\cdot\left(1+2+3+4\right)+...+\dfrac{1}{16}\cdot\left(1+2+3+...+16\right)\)
Tinh:
\(A=\dfrac{(13\dfrac{1}{4}-2\dfrac{5}{27}-10\dfrac{5}{6}).203\dfrac{1}{25}+46\dfrac{3}{4}}{(1\dfrac{3}{7}+\dfrac{10}{3}):\left(12\dfrac{1}{3}-14\dfrac{2}{7}\right)}\)
\(B=\dfrac{\left(81,624:4,8-4.505\right)^2+125.0,75}{\left\{\left[\left(0,44\right)^2:0,88+3,53\right]^2-\left(2,75\right)^2\right\}:0,52}\)
Tính
a, \(\left(\dfrac{1999}{2011}-\dfrac{2011}{1999}\right)-\left(\dfrac{-12}{1999}-\dfrac{12}{2011}\right)\)
b, \(\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right).....\left(1-\dfrac{1}{2015}\right)\)
1, thực hiện phép tính
\(\dfrac{\left(\dfrac{2}{5}\right)^9.10^9-\left(\dfrac{-9}{4}\right)^5:\left(\dfrac{-3}{16}\right)^{10}}{4^{12}+16^9}\)
2,CMR:\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+.......+\dfrac{1}{n^2}< \dfrac{2}{3}\)với n\(\ge\)4
Tính giá trị các biểu thức sau:
a, A = \(\left(3\dfrac{5}{6}-1\dfrac{1}{3}\right)\left(3\dfrac{4}{15}-2\dfrac{3}{5}\right)\)
b, B= \(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\) c, C = \(\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{6}\right)\left(1-\dfrac{1}{10}\right)\left(1-\dfrac{1}{15}\right)...\left(1-\dfrac{1}{210}\right)\)
