Cho \(A=1+\dfrac{3}{2^3}+\dfrac{4}{2^4}+\dfrac{5}{2^5}+...+\dfrac{100}{2^{100}}\). Chứng minh A < 2.
1) Cho A= \(\dfrac{1}{\sqrt{100}}+\dfrac{1}{\sqrt{101}}+\dfrac{1}{\sqrt{102}}+\dfrac{1}{\sqrt{103}}+\dfrac{1}{\sqrt{104}}\)
và B= \(\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)\left(1-\dfrac{1}{4^2}\right)....\left(1-\dfrac{1}{100^2}\right)\)
So sánh A và B.
Cho \(A=\left(\dfrac{1}{2^2}-1\right)\left(\dfrac{1}{3^2}-1\right)\left(\dfrac{1}{4^2}-1\right)...\left(\dfrac{1}{100^2}-1\right)\) thì \(A< \dfrac{1}{2}\)
Cmr \(\dfrac{1}{2^2}+\dfrac{1}{2^4}+.......+\dfrac{1}{2^{100}}< \dfrac{1}{3}\)
GIÚP MIK NHÉ,MIK Cần GẤP NGAY BÂY GIỜ
Chứng minh rằng:
\(\dfrac{1}{7^2}-\dfrac{1}{7^4}+...+\dfrac{1}{7^{4n-2}}-\dfrac{1}{7^{4n}}+...+\dfrac{1}{7^{98}}+\dfrac{1}{7^{100}}< \dfrac{1}{50}\)
Tính tổng: \(A=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{99}}+\dfrac{1}{3^{100}}\)
A= \(\left(\dfrac{1}{2}-1\right)\)\(\left(\dfrac{1}{3}-1\right)\).........\(\left(\dfrac{1}{10}-1\right)\). So sánh A với \(\dfrac{-1}{9}\)
B= \(\left(\dfrac{1}{4}-1\right)\)\(\left(\dfrac{1}{9}-1\right)\)...........\(\left(\dfrac{1}{100}-1\right)\). So sánh B với \(\dfrac{-11}{21}\)
Bài 1: Tính
A=\(\left(\dfrac{3}{7}-\dfrac{3}{17}+\dfrac{3}{37}\right):\left(\dfrac{5}{7}-\dfrac{5}{17}+\dfrac{5}{37}\right)+\dfrac{2}{5}\)
Bài 2: So sánh B với \(\dfrac{1}{2}\) biết:
B= \(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{100}}\)
tính
A=1+\(\dfrac{3}{2^3}\)+\(\dfrac{4}{2^4}\)+\(\dfrac{5}{2^5}\)+.....+\(\dfrac{100}{2^{100}}\)
