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Câu hỏi: Giá trị của biểu thức $T=\sum\limits_{k=1}^{2019}{C_{2019}^{k}{{.5}^{k}}}$ bằng
A. ${{6}^{2019}}-1.$
B. ${{6}^{2019}}-2019.$
C. ${{6}^{2019}}-2020.$
D. ${{6}^{2019}}.$
A. ${{6}^{2019}}-1.$
B. ${{6}^{2019}}-2019.$
C. ${{6}^{2019}}-2020.$
D. ${{6}^{2019}}.$
Ta có
$T=\left( \sum\limits_{k=1}^{2019}{C_{2019}^{k}{{.5}^{k}}+}C_{2019}^{0}{{.5}^{0}} \right)-C_{2019}^{0}{{.5}^{0}}=\sum\limits_{k=0}^{2019}{C_{2019}^{k}{{.5}^{k}}+}C_{2019}^{0}{{.5}^{0}}={{\left( 1+5 \right)}^{2019}}-1={{6}^{2019}}-1.$
$T=\left( \sum\limits_{k=1}^{2019}{C_{2019}^{k}{{.5}^{k}}+}C_{2019}^{0}{{.5}^{0}} \right)-C_{2019}^{0}{{.5}^{0}}=\sum\limits_{k=0}^{2019}{C_{2019}^{k}{{.5}^{k}}+}C_{2019}^{0}{{.5}^{0}}={{\left( 1+5 \right)}^{2019}}-1={{6}^{2019}}-1.$
Đáp án A.