\(=\dfrac{-3}{2}\cdot\dfrac{-4}{3}\cdot...\cdot\dfrac{-101}{100}=-\dfrac{101}{2}\)
\(=\dfrac{-3}{2}\cdot\dfrac{-4}{3}\cdot...\cdot\dfrac{-101}{100}=-\dfrac{101}{2}\)
So sánh: (1/22 - 1).(1/32 - 1).(1/42 - 1)....(1/1002 - 1) với -1/2
Cho A=1/2 mũ 2 +1/2 mũ 4 +1/2 mũ 6 +....+ 1/2 mũ 100
Chứng minh a <1/3
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 \(A< \dfrac{1}{2}\)
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 \(\dfrac{-11}{21}\)
1+3/2^3+4/2^4+...+100/2^100
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
Cho \(A=1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2^{100}-1}\).
CMR: 50 <A < 100.
Cho M = 1+2+3/4 + 5+6+7/8 + ... + 97+98+99/100
P = 1+ 1/2 1/3 + ... + 1/25
Tính K = M/50-P
Rất mong các bạn trả lời nhanh hộ mình nhé!