1. tính A= \(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{899}{30^2}\)
2. tính B= \(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}...\frac{30}{62}.\frac{31}{64}\)
3. So sánh C= \(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)\)với \(\frac{1}{21}\)
4. So sánh D= \(\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right)...\left(1-\frac{1}{100}\right)\)với \(\frac{11}{19}\)
3.Tính hợp lí:
a,\(\frac{17}{5}.\frac{-31}{125}.\frac{1}{2}.\frac{10}{17}.\frac{-1}{2^3}\)
b,\(\left(\frac{11}{4}.\frac{5}{9}-\frac{4}{9}.\frac{11}{4}\right).\frac{8}{33}\)
c,\(\left(\frac{17}{28}+\frac{18}{29}-\frac{19}{30}-\frac{20}{31}\right).\left(\frac{-5}{12}+\frac{1}{4}+\frac{1}{6}\right)\)
4.Tìm tích:
a,\(\left(\frac{1}{2}+1\right)\left(\frac{1}{3}+1\right).....\left(\frac{1}{99}+1\right)\)
b,\(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right).....\left(\frac{1}{100}-1\right)\)
c,\(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}....\frac{899}{30^2}\)
AI CÒN THỨC THÌ GIÚP MIK VS,MIK ĐANG CẦN GẤP
1) Tính hợp lý
a)\(\frac{31}{23}-\left(\frac{7}{32}+\frac{8}{32}\right)\)
b)\(\left(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}\right)-\left(\frac{79}{67}-\frac{28}{41}\right)\)
c)\(\frac{38}{45}-\left(\frac{8}{45}-\frac{17}{51}-\frac{3}{11}\right)\)
d)\(\left(\frac{17}{28}+\frac{18}{29}-\frac{19}{30}-\frac{30}{31}\right).\left(-\frac{5}{12}+\frac{1}{4}+\frac{1}{6}\right)\)
1, tim x bết:
,\(\frac{\left(-5^4\right).\left(-15^2\right)-5^4.\left(-3^2.5\right)}{\left(-3^4\right).25^2-\left(-15^2\right).225.5}\)\(:\)\(\frac{x}{5}\)\(=\frac{-1}{6}\)
2, cho A=\(\frac{20}{30}+\frac{20}{70}+\frac{20}{126}+...+\frac{20}{798}\)
B=\(\left(\frac{41}{2}.\frac{42}{2}.\frac{43}{2}...\frac{80}{2}\right):\left(1.3.5...79\right)\)
So sánh A và B.
3, Tính nhanh.
\(\frac{0,875+\frac{1}{2}-7\%-\frac{1}{58}}{\frac{1}{25}-\frac{1}{2}-\frac{2}{7}+\frac{2}{203}}\)\(-125\%\)
HELP ME PLEASE......
1. cho biểu thức :
D = \(\frac{\left(2!\right)^2}{1^2}+\frac{\left(2!\right)^2}{3^2}+\frac{\left(2!\right)^2}{5^2}+...+\frac{\left(2!\right)^2}{2015^2}\)
so sánh D với 6
2. cho các số nguyên dương a,b,c,d thỏa mãn : ab = cd
Chứng minh rằng : A = an + bn + cn + dn là hợp số
với mọi n \(\in\)N
Tính
a/ \(\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)
b/ A= \(\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right)....\left(\frac{1}{2013^2}-1\right).\left(\frac{1}{1014^2}-1\right)\)
B=\(\frac{-1}{2}\)
So sánh A và B
Tính hợp lý các biểu thức sau: (tức tính nhanh)
\(A=49\frac{8}{23}-\left(5\frac{7}{32}+14\frac{8}{23}\right)\)
\(B=71\frac{38}{45}-\left(43\frac{38}{45}-1\frac{17}{57}\right)\)
\(C=\left(19\frac{5}{8}:\frac{7}{12}-13\frac{1}{4}:\frac{7}{12}\right).\frac{4}{5}\)
\(D=\left[\left(\frac{10}{15}-\frac{2}{3}\right):\frac{1}{7}\right].0,15-\frac{1}{4}\)
\(E=\frac{13}{30}+\frac{28}{45}.2\frac{1}{2}-\left[\left(\frac{1}{2}+\frac{1}{3}\right):\frac{53}{90}\right]:\frac{50}{53}\)
Nhanh nhé, mình cần gấp, 3 người nào nhanh nhất mk tặng cho 5 tik nhé!!!!
Cho A = \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
B = \(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{10}\right)\)
a) So sánh A và B
b) Chứng minh A = \(\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}\)
Thực hiện phép tính sao cho hợp lí nhất:
a)\(2\frac{3}{4}.\left(-0.4\right)-1\frac{3}{5}.2,75+1,2:\frac{4}{11}\)
b)\(\left(\frac{1}{2}+1\right).\left(\frac{1}{3}+1\right).\left(\frac{1}{4}+1\right).....\left(\frac{1}{31}+1\right)\)
c)\(\frac{930}{1+2+3+....+30}\)