Tính giá trị biểu thức
A = $(1-\frac{1}{1011}).(1-$ $\frac{2}{1011}).(1-$ $\frac{3}{1011})...(1-$ $\frac{2020}{1011})$
Lời giải
A = $(1-\frac{1}{1011}).(1-$ $\frac{2}{1011}).(1-$ $\frac{3}{1011})...(1-$ $\frac{2020}{1011})$
A = $(\frac{1011}{1011}-$ $\frac{1}{1011}).($ $\frac{1011}{1011}-$ $\frac{2}{1011})...($ $\frac{1011}{1011}-$ $\frac{3}{1011})... $ $(\frac{1011}{1011}-$ $\frac{2020}{1011})$
A = $\frac{1010}{1011}.$ $\frac{1009}{1011}.$ $\frac{1008}{1011}...$ $\frac{-1009}{1011}$
A = $\frac{1010.1009.1008... 0 . (-1) . (-2) ... (-1009)}{1011}$
A = 0
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