Nêu công thức tính các bài toán liên quan tới vận tốc dòng nước .

Tính \(\dfrac{P}{Q}\) biết:

P= \(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2012}\)

Q= \(\dfrac{1}{2011}+\dfrac{2}{2010}+\dfrac{3}{2009}+...+\dfrac{2010}{2}+\dfrac{2011}{1}\)

5 Tinh tong

S=\(\dfrac{3}{1.4}\)+\(\dfrac{3}{4.7}\)+\(\dfrac{3}{7.10}\)+...+\(\dfrac{3}{97.100}\)

\(\dfrac{1}{2}x+0,2x-x-\dfrac{1}{5}=2\dfrac{3}{5}\)

Cho goc bet xOy .Tren cung mot nua at phang bo chua tia xy ve goc ​​xOn=400;yOm=700

a) Ke ten cac cap goc ke bu trong hinh ve

b) Tinh goc ​mOn

c) Tia Om la tia phan giac cua goc nao?Vi sao?

Tìm x bt :

a) x + x - 1 + x - 2 +...+z - 50 = 255

b) \(\left(x-\dfrac{1}{3}\right)^2-\dfrac{1}{4}=0\)

c) -2x + 624 = 5y (x,y \(\in\) N )

d) \(\dfrac{x+5}{2}=\dfrac{8}{x+5}\)

e) x + ( x + 1 ) + ( x + 2 ) +...+ ( x + 30 ) =1240

f) ( x - 1 ) + ( x - 2 ) + ... + (x - 19 ) + ( x - 20 ) = -610

g) ( 7x - 11 )3 = ( -3 )2 . 15 + 208

TÍnh A=\(\dfrac{1}{1.2}-\dfrac{1}{1.2.3}+\dfrac{1}{2.3}-\dfrac{1}{2.3.4}+\dfrac{1}{3.4}-\dfrac{1}{3.4.5}+...+\dfrac{1}{99.100}-\dfrac{1}{99.100.101}\)

B=\(\dfrac{5}{1.2.3.4}+\dfrac{5}{2.3.4.5}+...+\dfrac{5}{98.99.100.101}\)

C=\(\dfrac{6}{1^2+2^2}+\dfrac{10}{2^2+3^2}+\dfrac{14}{3^2+4^2}+...+\dfrac{398}{99^2.100^2}\)

Cho \(S=2+2^2+2^4+2^6+...+2^{102}\)

a) Tính gọn S

b) Tìm số dư khi chia S cho 3

\(5^{2x+1}\times133+13\times5^{2x-1}=4750\)

Thu gọn các tổng sau:

a. A=8.5100.(\(\dfrac{1}{5}+\dfrac{1}{5^2}+...+\dfrac{1}{5^{100}}\)) +1

b. B=\(\dfrac{4}{3}-\dfrac{4}{3^2}+...-\dfrac{4}{3^{100}}\)