Tìm x biết \(\frac{x+2}{327}+\frac{x+3}{326}+\frac{x+4}{325}+\frac{x+5}{324}+\frac{x+349}{5}=0\)

CMR:\(\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+...+\frac{99}{100!}< 1\)

\(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{100}}>10\)

Tính \(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+4\right)+...+\frac{1}{20}\left(1+2+3+...+20\right)\)

Bài 1 : Thực hiện phép tính

(1) D = \(1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{16}\left(1+2+...+16\right)\)

(2) M =\(\frac{\frac{1}{99}+\frac{2}{98}+\frac{3}{97}+...+\frac{99}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)

Bài 2 : Tìm x biết

(1) \(x-\left\{x-\left[x-\left(-x+1\right)\right]\right\}=1\)

(2) \(\left[\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2016}\right]\cdot x=\frac{2015}{1}+\frac{2014}{2}+...+\frac{1}{2015}\)

(3) \(\frac{x}{\left(a+5\right)\left(4-a\right)}=\frac{1}{a+5}+\frac{1}{4-a}\)

(4) \(\frac{x+2}{11}+\frac{x+2}{12}+\frac{x+2}{13}=\frac{x+2}{14}+\frac{x+2}{15}\)

(5) \(\frac{x+1}{2015}+\frac{x+2}{2014}+\frac{x+3}{2013}+\frac{x+4}{2012}+4=0\)

Bài 3 : 

(1) Cho : A =\(\frac{9}{1}+\frac{8}{2}+\frac{7}{3}+...+\frac{1}{9}\); B =\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}\)

CMR : \(\frac{A}{B}\)Là 1 số nguyên

(2) Cho : D =\(\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+...+\frac{1}{2000}\)CMR : \(D< \frac{3}{4}\)

Bài 4 : Ký hiệu [x] là số nguyên lớn nhất không vượt quá x , gọi là phần nguyên của x.

VD : [1.5] =1 ; [3] =3 ; [-3.5] = -4

(1) Tính :\(\left[\frac{100}{3}\right]+\left[\frac{100}{3^2}\right]+\left[\frac{100}{3^3}\right]+\left[\frac{100}{3^4}\right]\)

(2) So sánh : A =\(\left[X\right]+\left[X+\frac{1}{5}\right]+\left[X+\frac{2}{5}\right]+\left[X+\frac{3}{5}\right]+\left[X+\frac{4}{5}\right]\)và B = [5x]. Biết x=3.7

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

Bài 1Tìm x biết

\(x-\frac{37}{45}=\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{41.45}\)

Bài 2 Tính giá trị các biểu thức sau 

a) A = \(\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{97}+\frac{1}{99}}{\frac{1}{1.99}+\frac{1}{3.97}+\frac{1}{5.95}+...+\frac{1}{97.3}+\frac{1}{99.1}}\)

b) B = \(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}{\frac{99}{1}+\frac{98}{2}+\frac{97}{3}+...+\frac{1}{99}}\)

1. So sánh:

a. 1 và \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+.....+\frac{1}{2^{50}}\)

b. \(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+.....+\frac{1}{3^{100}}\)với \(\frac{1}{2}\)

c. \(\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^6}+.....\frac{1}{4^{1000}}\)với \(\frac{1}{3}\)

2. Tìm x, biết:

a.\(\left(\frac{2}{5}-x\right):1\frac{1}{3}+\frac{1}{2}=-4\)

b.\(3-\frac{1-\frac{1}{2}}{1+\frac{1}{x}}=2\frac{2}{3}\)

c.\(4^x+4^{x+3}=4160\)

d.\(2^{x-1}+5.2^{x-2}=\frac{7}{32}\)

e.\(\frac{x-100}{24}+\frac{x-98}{26}+\frac{x-96}{24}=3\)

g.\(\frac{x-1}{65}+\frac{x-3}{63}+=\frac{x-5}{61}+\frac{x-7}{59}\)

Tìm x thoả mãn:

a)\(\frac{1}{2}x-\frac{3}{4}x-\frac{7}{3}=-\frac{5}{6}\)

b)\(\frac{4}{5}x-x-\frac{3}{2}x+\frac{4}{3}=\frac{1}{2}-\frac{6}{5}\)

c)\(\frac{1}{1.2}+\frac{1}{2.3}+......+\frac{1}{x.\left(x+1\right)}=\frac{2009}{2010}\)

d)\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=1\frac{2013}{2015}\)

e)\(\frac{1}{3.5}+\frac{1}{5.7}+.....+\frac{1}{\left(2x+1\right)\left(2x+3\right)}=\frac{100}{609}\)

Bài 1: Tính nhanh

a) \(\frac{2}{3.5}\)+\(\frac{2}{5.7}\)+\(\frac{2}{7.9}\)+...+\(\frac{2}{19.21}\)

b) \(\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right).....\left(1+\frac{1}{99}\right)\)

c) \(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}{\frac{1}{99}+\frac{2}{98}+\frac{3}{97}+...+\frac{98}{2}+\frac{99}{1}}\)

Bài 2. Tìm x, biết:

a) \(\frac{x-2}{20}=\frac{5}{2-x}\)

b)  \(\left(\frac{x}{3}+\frac{1}{2}\right)\left(75\%-1\frac{1}{2}x\right)=0\)

Mk cảm ơn nhé. Các bn làm đc câu nào thì làm (nhất là b2)

a)  (1-\(\frac{1}{2}\)) x (1-\(\frac{1}{3}\)) x (1-\(\frac{1}{4}\)) x .......... x (1-\(\frac{1}{99}\))

b) (1+\(\frac{1}{2}\)) x (1+\(\frac{1}{3}\)) x (1+\(\frac{1}{4}\)) x ........ x (1+\(\frac{1}{99}\))

c) (1-\(\frac{1}{2^2}\)) x (1-\(\frac{1}{3^2}\)) x (1-\(\frac{1}{4^2}\) ) x ....... x (1-\(\frac{1}{99^2}\))