\(1+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{n^2}
trong hinh anh giong nhau ghe nhi
Chứng minh:
\(A=1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+......+\frac{1}{n^2}<2-\frac{1}{n}\)
Cho n>=2 .Chứng minh:\(\frac{1}{2}
chứng minh
\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{n^2}
1. Hãy tính tổng:
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{n\left(n+1\right)}\)
2. Chứng minh:\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{n^2}<1\)
Chứng minh:
a, M= \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{n^2}< 1\)
b, \(\frac{1}{6}< \frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{100^2}< \frac{1}{4}\)
Chứng minh rằng:
a)\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2010^2}\)<1
b)\(\frac{1}{2}+\frac{2}{2^2}+\frac{3}{2^3}+\frac{4}{2^4}+...+\frac{100}{2^{100}}\)<2
c)\(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+...+\frac{100}{3^{100}}\)<\(\frac{3}{4}\)
d)\(\frac{1}{3^3}+\frac{1}{4^3}+\frac{1}{5^3}+...+\frac{1}{n^3}\)<\(\frac{1}{12}\)\(\left(n\in N;n\ge3\right)\)
e)\(\frac{3}{4}+\frac{5}{36}+\frac{7}{144}+...+\frac{2n+1}{n^2\left(n+1\right)^2}\)<1 (n nguyên dương)
g)\(\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+...+\frac{1}{2048}\)>3
h)\(\left(\frac{2}{1}\right)\left(\frac{4}{3}\right)\left(\frac{6}{5}\right)...\left(\frac{200}{199}\right)\)
Chứng minh: \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{n^2}<1\)với n thuộc N sao
