Các câu hỏi tương tự
Cho A = \(\frac{1}{1x2^2}+\frac{1}{2x3^2}+\frac{1}{3x4^2}+...+\frac{1}{49x50^2}\)
B = \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}\)
CM A < \(\frac{1}{2}\) < B
tính:
a) \(\frac{1^2}{1x2}+\frac{2^2}{2x3}+\frac{3^2}{3x4}+...+\frac{100^2}{100x101}\)
b) \(\frac{2^2}{1x3}+\frac{3^2}{2x4}+\frac{4^2}{3x5}+...+\frac{59^2}{58x60}\)
Bài 2:Tính tổng
a) \(\frac{1}{2x3}+\frac{1}{3x4}+....+\frac{1}{49x50}\)
Tính nhanh:
A= 1/2+1/2^2+1/2^3+....+1/2^100
B=3^2/2x4+3^2/4x6+3^2/6x8+....+3^2/198x200
C=\(\frac{\frac{2017}{1}+\frac{2017}{2}+\frac{2017}{3}+...+\frac{2017}{2017}}{\frac{2016}{1}+\frac{2015}{2}+\frac{2014}{3}+...+\frac{1}{2016}}\)
D=1x2+2x3+3x4+4x5+...+48x49
E=\(^{1^2+2^2+3^2+...+48^2}\)
F=1x49+2x48+3x47+...+48x2+49x1
Chứng minh rằng :\(\frac{1}{2}+\frac{1}{3x4}+\frac{1}{5x6}+.....+\frac{1}{49x50}=\frac{1}{26}+\frac{1}{27}+\frac{1}{28}+...+\frac{1}{50}\) [chú ý x là dấu nhân]
Chứng minh rằng : \(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{49x50}<1\)
Làm nhanh mình lick cho !
b, B = 1\(\frac{1}{1x2}+\frac{1}{2x3}+......+\frac{1}{99x100}\)
c, C = \(\frac{1}{1x2}+\frac{1}{2x3}+......+\frac{1}{n\left(n+1\right)}\)
d, D = 1 + 2 + 3 + ......+ n
Tìm y biết:
a) (y+2):5-5x5=378
b) (7,56x0,99+7,56x0,01)x(y+2)=18,9
c) (y+\(\frac{1}{1x2}\))+(y+\(\frac{1}{2x3}\))+(y+\(\frac{1}{3x4}\))+...+(y+\(\frac{1}{2013x2014}\))=\(\frac{2013}{2014}\)
Tính nhanh các biểu thức sau:
a) A = \(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{19}\)
b) B = \(\frac{2}{3}+\frac{2}{6}+\frac{2}{9}+...+\frac{2}{90}\)
c) C = \(\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+...+\frac{1}{50^2}\)