Bai 1; a) Cho \(B\) = \(\frac{1}{2}\)+ (\(\frac{1}{2}\))2 + (\(\frac{1}{2}\))3 + (\(\frac{1}{2}\))4 + ... + (\(\frac{1}{2}\))98 + (\(\frac{1}{2}\))99 . Chứng minh rằng \(B\) \(< 1\)
b) Cho \(C\) = \(\frac{1}{3}\)+ \(\frac{1}{3^2}\)+ \(\frac{1}{3^3}\)+...+ \(\frac{1}{3^{98}}\)+ \(\frac{1}{3^{99}}\). Chứng minh rằng \(C\) \(< \)\(\frac{1}{2}\)
Bai 2;Chứng minh rằng;
a) \(\frac{3}{1^2.2^2}\)+ \(\frac{5}{2^2.3^2}\)+ \(\frac{7}{3^2.4^2}\)+ ... + \(\frac{19}{9^2.10^2}\)\(< \)\(1\)
b) \(\frac{1}{3}\)+ \(\frac{2}{3^2}\)+\(\frac{3}{3^3}\)+ ... + \(\frac{99}{3^{99}}\)+ \(\frac{100}{3^{100}}\)\(< \frac{3}{4}\)