tÍNH:
a, \(4\frac{25}{16}+25.\left(\frac{9}{16}-\frac{117}{64}\right):\frac{27}{8}\)
b, -15,5x20,8+3,5x9,2-15,5x9,2+3,5x20,8
c, \(\frac{5}{16}:0,125+1,456:\frac{7}{25}+4\frac{1}{2}.0,8\)
12)\(0,2.\frac{15}{36}-\left(\frac{2}{5}+\frac{2}{3}\right):1\frac{1}{5}\)
13)\(1\frac{13}{15}.0,75-\left(\frac{8}{15}+0,25\right).\frac{24}{27}\)
16)\(\frac{1}{2}+\frac{3}{4}-\left(\frac{3}{4}-\frac{4}{5}\right).\left(-2,75\right)\)
18)\(\left(\frac{7}{8}-\frac{3}{4}\right).1\frac{1}{3}-\frac{2}{7}.\left(3.5\right)^2\)
22)\(1\frac{13}{15}.0,75-\left(\frac{11}{20}+25\%\right):\frac{7}{3}\)
23)\(\frac{\left(\frac{2}{3}-0,75\right).\left(0,2-\frac{2}{5}\right)}{\frac{5}{9}-1\frac{1}{12}}\)
33)\(\left(25\%+\frac{1}{3}+0,75\right):\left(4\frac{3}{4}-3\frac{1}{2}\right)\)
35)\(\left(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}\right).\left(\frac{1}{6}-\frac{1}{8}-\frac{1}{24}\right)\)
\(1\frac{13}{15}.0,75-\left(\frac{8}{15}+25\%\right).\frac{24}{47}-3\frac{12}{13}:3\)
Tìm x
\(4\frac{1}{3}.\left(\frac{1}{6}-\frac{1}{2}\right)\le x\le\frac{2}{3}.\left(\frac{1}{3}-\frac{1}{2}-\frac{3}{4}\right)\)
Cho \(A=\frac{\left(3\frac{2}{15}+\frac{1}{15}\right):2\frac{1}{2}}{\left(5\frac{3}{7}-2\frac{1}{4}\right):4\frac{43}{56}}\)
\(B=\frac{1;2:\left(1\frac{1}{5}:1\frac{1}{4}\right)}{0,32+\frac{2}{25}}\)
So sánh A và B
\(E=\frac{1}{25.27}+\frac{1}{27.29}+...+\frac{1}{73.75}.\)
\(F=\frac{15}{90.94}+\frac{15}{94.98}+...+\frac{15}{146.150}\)
\(G=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
Bài 2
\(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{100^2}.\)
CMR A<\(\frac{3}{4}\)
Chứng minh \(\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{2}\)\(\frac{1}{2}\)
b,\(\frac{1}{^{2^2}}+\frac{1}{4^2}+\frac{1}{6^2}+...+\frac{1}{100^2}< \frac{1}{2}\)
c,\(\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{2499}{2500}>48\)
d,\(\frac{1}{6}< \frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{100^2}< \frac{1}{4}\)
1) tính giá trị biểu thức:
a)-1\(\frac{5}{7}.15+\frac{2}{7}\left(-15\right)+\left(-105\right)\left(\frac{2}{3}-\frac{4}{5}+\frac{1}{7}\right)\)
b)\(\frac{3}{14}:\frac{1}{28}-\frac{13}{21}:\frac{1}{28}+\frac{49}{42}:\frac{1}{28}-6\)
c)\(4.\left(-\frac{1}{2}\right)^3-2.\left(-\frac{1}{2}\right)^2+3.\left(-\frac{1}{2}\right)+1\)
A=\(\frac{\left(3\frac{2}{15}+\frac{1}{15}\right):2\frac{1}{2}}{\left(5\frac{3}{7}-2\frac{1}{4}\right):4\frac{43}{56}}\)
B=\(\frac{1,2:\left(1\frac{1}{5}\cdot1\frac{1}{4}\right)}{0,32+\frac{2}{25}}\)
Chứng minh A=B
A=(-1,7).2,3+1,7.(-3,7)-1,7.3-0,17:\(\frac{1}{10}\)
B=\(\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right).\left(\frac{1}{4}-1\right)...\left(\frac{1}{2017}-1\right)\)
C=\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{899}{900}\)
D=\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{9999}\)
E=\(1-3+3^2-3^3+...+3^{2016}-3^{2017}+3^{2018}\)
G=\(2+2^2+2^3+...+2^{60}\)