Tính \(A=\left(\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\frac{1}{14\cdot19}+...+\frac{1}{44\cdot49}\right)\cdot\frac{1-3-5-7-...-49}{89}\)
\(B=\frac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^{10}\cdot6^{19}-7\cdot2^{29}\cdot27^6}-\frac{2^{19}\cdot27^3+15\cdot4^9\cdot9^4}{6^9\cdot2^{10}+12^{10}}\)
bài này không khó. Nhưng đánh máy để giải cho bạn thì thực sự khó
câu 1: so sánh A và B
A=\(\frac{10^{15}+1}{10^{16}+1}\)
B=\(\frac{10^{16}+1}{10^{17}+1}\)
Câu 2:so sánh 637 và 1612
( \(\frac{1}{32}\))7 và( \(\frac{1}{16}\))9
câu 3: so sánh
A=\(\frac{10^{1992}+1}{10^{1991}+1}\), B=\(\frac{10^{1993}+1}{10^{1992}+1}\)
câu 4 : CMR :\(\frac{1}{4}\)+\(\frac{1}{16}\)+\(\frac{1}{36}\)+\(\frac{1}{64}\)+.....+\(\frac{1}{10000}\)<\(\frac{1}{2}\)
câu 5 A=1+\(\frac{2^2}{3^2}\)+\(\frac{2^2}{5^2}\)+\(\frac{2^2}{7^2}\)+.......+\(\frac{2^2}{2009^2}\)
So sanh A với 3
câu 6 cho S = \(\frac{3}{4}\)+\(\frac{8}{9}\)+\(\frac{15}{16}\)+......+\(\frac{n^2-1}{n^2}\)
CMR với mọi số tự nhiên n\(\ge\)2 thì 3 không thể là số nguyên
Tính \(\frac{M}{N}\)biết :
M = \(\frac{2}{7\cdot19}+\frac{6}{7\cdot27}+\frac{1}{4\cdot9}+\frac{7}{12\cdot43}+\frac{8}{17\cdot43}\)
N = \(\frac{9}{7\cdot19}+\frac{5}{7\cdot33}+\frac{7}{10\cdot33}+\frac{11}{10\cdot31}\)
\(M=\frac{32}{323}\) \(N=\frac{86}{589}\) \(\frac{M}{N}=\frac{496}{731}\)
Tính Nhanh:
D = \(\frac{4}{3\cdot7}-\frac{4}{7\cdot11}+\frac{4}{11\cdot15}-\frac{4}{15\cdot19}+\frac{4}{19\cdot23}-\frac{4}{23\cdot27}\)
sắp xếp các phân số sau theo thứ tự từ bé đến lớn :
a ) \(\frac{7}{10}\ ,\ \frac{10}{13}\ ,\ \)\(\frac{4}{7}\ ,\ \frac{1}{4}\ ,\ \frac{13}{16}\ ,\ \frac{16}{19}\ .\)
b ) \(\frac{13}{10}\ ,\ \frac{17}{14}\ ,\ \frac{11}{8}\ ,\ \frac{8}{5}\ ,\ \frac{18}{15}\ ,\ \frac{21}{18}\)
1.tính các biểu thức sau bằng một cách hợp lí
a.\(\frac{108}{119}.\frac{107}{211}+\frac{108}{119}.\frac{104}{211}\)
b.\(\frac{15}{19}.\frac{27}{33}+\frac{15}{19}.\frac{19}{33}-\frac{15}{19}.\frac{13}{33}\)
c.\(\frac{-4}{5}.\frac{13}{10}+\frac{-4}{5}.\frac{7}{10}-\frac{-4}{5}\)
d.\(\frac{\frac{-2}{7}-\frac{-2}{15}+\frac{-2}{39}}{\frac{5}{7}-\frac{5}{15}+\frac{5}{39}}\)
e.\(\frac{3}{5}.\frac{15}{7}-\frac{15}{7}.\frac{8}{5}\)
f.\(\frac{2}{3}+\frac{1}{3}.\left(\frac{-4}{9}+\frac{5}{6}\right):\frac{7}{12}\)
h.\(\frac{\frac{3}{5}+\frac{3}{7}-\frac{3}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{11}}\)
g.\(\frac{3}{-4}+\frac{2}{7}+\frac{-1}{4}+\frac{5}{7}+\frac{21}{22}.\frac{66}{7}\)
k.\(\frac{27.18+27.103-120.27}{15.33+33.12}\)
l.\(\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{9}-\frac{4}{11}}\)
\(a.\frac{108}{119}.\frac{107}{211}+\frac{108}{119}.\frac{104}{211}=\frac{108}{119}.\left(\frac{107}{211}+\frac{104}{211}\right)=\frac{108}{119}.1=108\)
A=\(\frac{\left(\frac{3}{10}-\frac{4}{15}-\frac{7}{20}\right).\frac{5}{19}}{\left(\frac{1}{14}+\frac{1}{7}-\frac{-3}{35}\right).\frac{-4}{3}}\)
Tính giá trị của các biểu thức sau một cách hợp lý:
a)A=\(\frac{3^{10}.11+3^{10}.5}{3^9.2^4+2^{10}.13}+\frac{2^{10}.13+2^{10}.65}{2^8.104}\)
b)B=\(\frac{12-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}:\frac{3+\frac{3}{13}+\frac{3}{169}+\frac{3}{91}}{7+\frac{7}{13}+\frac{7}{169}+\frac{7}{91}}\)
1.tính giá trị biểu thức sau một cách hợp lí nếu có
a)\(\frac{1}{3}.\frac{4}{5}+\frac{1}{3}.\frac{6}{5}-\frac{5}{3}\)
b)\(\frac{4}{19}.\frac{-3}{7}+\frac{-3}{7}.\frac{15}{19}+\frac{5}{7}\)
c)\(\frac{6}{7}.\frac{10}{9}+\frac{1}{7}.\frac{10}{9}-\frac{8}{9}\)
a. \(\frac{1}{3}.\frac{4}{5}+\frac{1}{3}.\frac{6}{5}-\)
\(=\frac{1}{3}(\frac{4}{5}+\frac{6}{5})-\frac{5}{3}\)
\(=\frac{1}{3}.2-\frac{5}{3}\)
\(=\frac{2}{3}-\frac{5}{3}\)
\(=-\frac{1}{1}\)
c. \(\frac{6}{7}.\frac{10}{9}+\frac{1}{7}.\frac{10}{9}-\frac{8}{9}\)
\(=\frac{10}{9}\left(\frac{6}{7}+\frac{1}{7}\right)-\frac{8}{9}\)
\(=\frac{10}{9}.1-\frac{9}{8}\)
\(=\frac{10}{9}-\frac{9}{8}\)
\(=-\frac{1}{72}\)
\(b\).\(\frac{4}{19}.\frac{-3}{7}+\frac{-3}{7}.\frac{15}{19}+\frac{5}{7}\)
\(=\frac{-3}{7}\left(\frac{4}{19}+\frac{15}{19}\right)+\frac{5}{7}\)
\(=\frac{-3}{7}+\frac{5}{7}\)
\(=\frac{2}{7}\)
