Chứng minh rằng: \(A=\frac{1}{3^2}-\frac{1}{3^4}+...+\frac{1}{3^{4n-2}}-\frac{1}{3^{4n}}+...+\frac{1}{3^{98}}-\frac{1}{3^{100}}

Chứng minh rằng:

A=\(\frac{1}{3^2}+\frac{1}{3^4}+.......+\frac{1}{3^{4n-2}}+\frac{1}{3^{4n}}+....+\frac{1}{3^{98}}-\frac{1}{3^{100}}\)< 0,1

Chứng minh rằng

A= \(\frac{1}{3^{^2}}\)- \(\frac{1}{3^4}\)+.......+ \(\frac{1}{3^{4n-2}}\)- \(\frac{1}{3^{4n}}\)+.......+ \(\frac{1}{3^{98}}\)- \(\frac{1}{3^{100}}\)< 0,1

Chứng minh rằng:

a,\(\frac{5}{3.7}+\frac{5}{7.11}+\frac{5}{11.15}+...+\frac{5}{\left(4n-1\right).\left(4n+3\right)}=\frac{5n}{3.\left(4n+3\right)}\)

b,\(\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+100}< \frac{1}{4}\)

Chứng minh rằng : \(\frac{1}{7^2}-\frac{1}{7^4}+...+\frac{1}{7^{4n-2}}-\frac{1}{7^{4n}}+...+\frac{1}{7^{98}}-\frac{1}{7^{100}}< \frac{1}{50}\)

Chứng minh rằng \(\frac{1}{8^2}-\frac{1}{8^4}+...+\frac{1}{8^{4n-2}}-\frac{1}{8^{4n}}+...+\frac{1}{8^{98}}-\frac{1}{8^{100}}\)

Bài 3:

So sánh A=\(\frac{1}{3^2}+\frac{1}{3^4}+\frac{1}{3^6}+\frac{1}{3^8}+...+\frac{1}{3^{2n+3}}+\frac{1}{3^{4n}}+...+\frac{1}{3^{98}}-\frac{1}{3^{100}}\)với \(\frac{1}{10}\)

Cho M =\(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}\) .Hãy chứng minh M<\(\frac{3}{16}\)

Câu 2 Chứng minh rằng :

\(\frac{1}{7^2}-\frac{1}{7^4}+...+\frac{1}{7^{98}}-\frac{1}{7^{100}}< \frac{1}{50}\)

Chứng minh:

\(\frac{1}{7^2}-\frac{1}{7^4}+...+\frac{1}{4n-2}+\frac{1}{4n}+...+\frac{1}{98}+\frac{1}{100}<\frac{1}{50}\)