Tính nhanh : \(1+\dfrac{1}{2}+\dfrac{1}{4}+....+\dfrac{1}{2^{2005}}\)
Giải rõ chi tiết nhá
Cho \(S=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+................+\dfrac{1}{48}+\dfrac{1}{49}+\dfrac{1}{50}\) và \(P=\dfrac{1}{49}+\dfrac{2}{48}+\dfrac{3}{47}+..........+\dfrac{48}{2}+\dfrac{49}{1}\)
Tính \(\dfrac{S}{P}\)
Help me!!!!!!!!!!!
Bài 1: Cho b \(\in\) N, b > 1
Chứng minh: \(\dfrac{1}{b}-\dfrac{1}{b+1}< \dfrac{1}{b^2}< \dfrac{1}{b-1}-\dfrac{1}{b}\)
Bài 2: Cho S = \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+.....+\dfrac{1}{9^2}\)
Chứng minh: \(\dfrac{2}{5}< S< \dfrac{8}{9}\)
-Giúp tớ với, bí quá :<
cho B=\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{100^2}\)
so sánh B với 1
So sánh
A=\(\frac{2005^{2014}+1}{2005^{2015}+1}\)
với
B=\(\frac{2005^{2015}+1}{2005^{2016}+1}\)
TÍNH:
\(\dfrac{27}{10}+\dfrac{291}{100}+\dfrac{38}{100}+\dfrac{547}{1000}\dfrac{893}{10000}\)
TÍNH NHANH
a, \(\dfrac{2006\times2005-1}{2004\times2006+2005}\)\
b, \(18\times\left(\dfrac{19191919+88888}{21212121+99999}\right)\)
So sánh S với 2
S = \(\dfrac{1}{2}+\dfrac{2}{2^2}+\dfrac{3}{2^3}+........+\dfrac{2017}{2^{2017}}\)
So sánh A vs \(\dfrac{3}{4}\)
Cho A= \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+......+\dfrac{1}{200^2}\)
\(B=1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+....+\dfrac{1}{2^{99}}\)
So sánh B với 50
