Tuyển Cộng tác viên Hoc24 nhiệm kì 26 tại đây: https://forms.gle/dK3zGK3LHFrgvTkJ6
\(\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right).\left(\frac{1}{4^2}-1\right)...\left(\frac{1}{100^2}-1\right)\)
\(CMR:A< -\frac{1}{2}\)
Cho M=1+\(\frac{1}{2}+\frac{1}{3}+..................\frac{1}{2^{100}-1}\)
CMR:a, M<100
b, M>50
nhanh nhé
A=\(\frac{1}{3}\)+\(\frac{2}{3^2}\)+\(\frac{3}{3^3}\)+...+\(\frac{100}{3^{100}}\)
CMR:A<\(\frac{3}{4}\)
Ai đúng và nhanh nhất mk tích nhé !
1) Cho \(A=\frac{9}{10!}+\frac{9}{11!}+\frac{9}{12!}+...+\frac{9}{1000!}.CMR:A< \frac{1}{9!}\)
2) \(CMR:\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< \frac{1}{2}\)
Ai giúp mk sẽ đc thưởng 3 tick , phải ghi chép đầy đủ nha
A=\(\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+...+\frac{99}{5^{100}}\) CMR:A<\(\frac{1}{16}\)
\(Cho\)\(A=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2^{100}-1}\)
\(CMR:a,A< 100\)
\(b,A>50\)
1, Tính \(\frac{1}{2}-\left(\frac{1}{3}+\frac{2}{3}\right)+\left(\frac{1}{4}+\frac{2}{4}+\frac{3}{4}\right)-\left(\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+\frac{4}{5}\right)+...+\left(\frac{1}{100}+\frac{2}{100}+\frac{3}{100}+...+\frac{99}{100}\right)\)2,Tính \(\left(1-\frac{1}{2^2}\right)x\left(1-\frac{1}{3^2}\right)x\left(1-\frac{1}{4^2}\right)x...x\left(1-\frac{1}{n^2}\right)\)
Chứng minh rắng
a) \(\frac{1}{2}+\frac{2}{2^2}+\frac{3}{2^3}+..+\frac{100}{2^{100}}<2\)
b) \(\frac{4}{3}<\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+..+\frac{1}{70}<\frac{5}{2}\)
c) \(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+...+\frac{100}{3^{100}}<\frac{3}{4}\)
a)\(\frac{1}{10^2}+\frac{1}{11^2}+\frac{1}{12^2}+...+\frac{1}{100^2}<\frac{3}{4}\)
b)\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}<\frac{99}{100}\)
c)\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}<\frac{3}{4}\)
