Đáp án + Giải thích các bước giải:
$\text{a, Ta có:}$
$\text{(1 + $\dfrac{1}{2}$)(1 + $\dfrac{1}{3}$)(1 + $\dfrac{1}{4}$) .... (1 + $\dfrac{1}{100}$)}$
= $\text{$\dfrac{3}{2}$ . $\dfrac{4}{3}$ . $\dfrac{5}{4}$ . .... . $\dfrac{101}{100}$}$
= $\text{$\dfrac{3}{2}$ . $\dfrac{4}{3}$ . $\dfrac{5}{4}$ . .... . $\dfrac{101}{100}$}$
= $\text{$\dfrac{101}{2}$}$
$\text{b, Ta có:}$
$\text{ $\dfrac{1^{2} }{1 .2}$ . $\dfrac{2^{2} }{2 .3}$ . ... . $\dfrac{100^{2} }{100 .101}$}$
= $\text{ $\dfrac{1^{2} }{1 .2}$ . $\dfrac{2^{2} }{2 .3}$ . ... . $\dfrac{100^{2} }{100 .101}$}$
= $\text{$\dfrac{1}{2}$ . $\dfrac{2}{3}$ . ... . $\dfrac{100}{101}$}$
= $\text{$\dfrac{1}{101}$}$
