\(A=1\frac{1}{3}.2\frac{1}{4}+1\frac{1}{3}.3\frac{3}{4}\)
\(A=1\frac{1}{3}.\left(2\frac{1}{4}+3\frac{3}{4}\right)\)
\(A=1\frac{1}{3}.6\)
\(A=8\)
Số dư của A= \(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{98}\)x 2 x3 x4x ...98 khi chia cho 99 là
bài 1:
tìm n biết: 5n+7 chia hết 3n+2
bài 2:
1, tìm chữ số tận cùng của:
a,57^1999
b,93^1999
2, Cho A= 999993^1999 - 555557^1997
chứng minh rằng: A chia hết cho 5
bài 3:chứng minh rằng:
a) \(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}< \frac{1}{3}\)
b)\(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}< \frac{3}{16}\)
Bài 5:Tìm x biết:
a)11.(x-6)=4.x+11
b)\(4\frac{1}{3}.\left(\frac{1}{6}-\frac{1}{2}\right)\le x\le\frac{2}{3}.\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{4}\right)\)với x\(\in\)Z
c)|x-3|+1=x
tìm x:
a) \(\overline{x3}+\overline{3x}=12\times11\)
b) \(4\frac{3}{4}-\left(\frac{1}{2}+x\right)\div4\frac{2}{3}=2\frac{1}{2}\)
1 tìm x biết ;
a, 0-|x + 1| = 5
b, 2 - | \(\frac{3}{4}\)- x | = \(\frac{7}{12}\)
c, 2 | \(\frac{1}{2}\)x - \(\frac{1}{3}\)| - \(\frac{3}{2}\)= \(\frac{1}{4}\)
d, | x - \(\frac{1}{3}\)| = \(\frac{5}{6}\)
e, \(\frac{3}{4}\)- 2 | 2x - \(\frac{2}{3}\)| = 2
f, \(\frac{2x-1}{2}\)= \(\frac{5+3x}{3}\)
1 tìm x biết ;
a, 0-|x + 1| = 5
b, 2 - | \(\frac{3}{4}\)- x | = \(\frac{7}{12}\)
c, 2 | \(\frac{1}{2}\)x - \(\frac{1}{3}\)| - \(\frac{3}{2}\)= \(\frac{1}{4}\)
d, | x - \(\frac{1}{3}\)| = \(\frac{5}{6}\)
e, \(\frac{3}{4}\)- 2 | 2x - \(\frac{2}{3}\)| = 2
f, \(\frac{2x-1}{2}\)= \(\frac{5+3x}{3}\)
1.Cho A =\(\frac{5n-11}{n-2}\left(n\inℤ\right)\)
a. Tìm điều kiện n để A là phân số
b.Tìm n \(\inℤ\)để A có giá trị nguyên
c.Tìm giá trị lớn nhất của A
2.Tìm x
a. \(\frac{3}{4}\times\left(\frac{1}{2}x+\frac{1}{3}\right)-\frac{1}{2}=\frac{2}{3}x-\frac{1}{4}\)
b.\(\frac{2}{3}x-3x+\frac{1}{5}=\frac{3}{2}\left(x-\frac{1}{4}\right)-\frac{3}{2}\)
3.a.Chứng tỏ :
\(\frac{1}{7^2}+\frac{1}{8^2}+..................+\frac{1}{99^2}< \frac{1}{6}\)
b.Chứng tỏ:
\(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+............+\frac{1}{23}< 3\)
Bài 2: a.Tính
\(\frac{1}{4}-\frac{1}{7}=\frac{3}{4.7};_{ }_{ }\frac{1}{7}-\frac{1}{10}=\frac{3}{7.10};_{ }_{ }\frac{1}{10}-\frac{1}{13}=\frac{3}{10.13};_{ }_{ }\frac{1}{13}-\frac{1}{16}=\frac{3}{13.16};_{ }....._{ }\frac{1}{x}-\frac{1}{x+3}=\frac{3}{x\left(x+3\right)}\)Qui luật: \(\frac{m}{a\left(a+m\right)}=\frac{1}{a}-\frac{1}{a+m}\)
b. A = \(\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{x\left(x+3\right)}\)
3A = \(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{x\left(x+3\right)}\)
3A = \(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{x}-\frac{1}{x+3}\)
3 A = \(\frac{1}{4}-\frac{1}{x+3}\)
\(\frac{63}{764}.3=\frac{1}{4}-\frac{1}{x+3}\)
\(\frac{189}{764}=\frac{1}{4}-\frac{1}{x+3}\)
\(\frac{1}{382}=\frac{1}{x+3}_{ }_{ }_{ }=>x=382-3=379\)
Tìm x thuộc Z
a)\(\frac{1}{3}+\frac{3}{35}< \frac{x}{210}< \frac{4}{7}+\frac{3}{5}+\frac{1}{3}\)
b)\(\frac{5}{3}+\frac{-14}{3}< x< \frac{8}{5}+\frac{18}{10}\)
c)\(\frac{1}{3}+\frac{-2}{5}+\frac{1}{6}+\frac{-1}{5}\subseteq x< -\frac{3}{4}+\frac{2}{7}+-\frac{1}{4}+\frac{3}{5}+\frac{5}{7}\)
\(\subseteq\)là lớn hơn hoặc bằng nha
Bài 1:Tìm \(x\in Z\)biết
\(A=\frac{3}{x-1}\)\(B=\frac{x-2}{x+3}\)\(C=\frac{2x+1}{x-3}\)
Bài 2:Chứng tỏ rằng:
\(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.....+\frac{1}{63}>2\)\(B=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}< 1\)
Bài 3:Tính hợp lí
\(A=\frac{\frac{3}{5}+\frac{3}{7}-\frac{3}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{11}}\)
\(B=\frac{7}{4}\left(\frac{3333}{1212}+\frac{3333}{2020}+\frac{3333}{3030}+\frac{3333}{4242}\right)\)
