Đáp án:
Giải thích các bước giải:
a)$N = \frac{{{{19}^{31}} + 5}}{{{{19}^{32}} + 5}} < \frac{{{{19}^{31}} + 5 + 14}}{{{{19}^{32}} + 5 + 14}} = \frac{{19.({{19}^{30}} + 1)}}{{19({{19}^{31}} + 1)}} = \frac{{{{19}^{30}} + 1}}{{{{19}^{31}} + 1}} < \frac{{{{19}^{30}} + 5}}{{{{19}^{31}} + 5}} = M$
b)\[\begin{array}{l}
E = 1 + \frac{1}{2}(1 + 2) + \frac{1}{3}(1 + 2 + 3) + ... + \frac{1}{{200}}(1 + 2 + ... + 200)\\
= 1 + \frac{1}{2}.\frac{{2.3}}{2} + \frac{1}{3}\frac{{3.4}}{2} + ... + \frac{1}{{200}}.\frac{{200.201}}{2} = \frac{2}{2} + \frac{3}{2} + \frac{4}{2} + ... + \frac{{201}}{2} = \frac{{2 + 3 + 4 + ... + 201}}{2} = \frac{{200.203}}{2} = 20300
\end{array}\]
