Câu 25: \(E=-\frac13+\frac{1}{3^2}-\frac{1}{3^3}+\frac{1}{3^4}-\cdots+\frac{1}{3^{50}}-\frac{1}{3^{51}}\)
=>3E=\(-1+\frac13-\frac{1}{3^2}+\frac{1}{3^3}-\cdots+\frac{1}{3^{49}}-\frac{1}{3^{50}}\)
=>3E+E=\(-1+\frac13-\frac{1}{3^2}+\cdots-\frac{1}{3^{50}}-\frac13+\frac{1}{3^2}-\frac{1}{3^3}+\cdots-\frac{1}{3^{51}}\)
=>4E=\(-1-\frac{1}{3^{51}}=\frac{-3^{51}-1}{3^{51}}\)
=>\(E=\frac{-3^{51}-1}{4\cdot3^{51}}\)
=>Chọn D
Câu 24; \(D=\left(-\frac17\right)^0+\left(-\frac17\right)^1+\cdots+\left(-\frac17\right)^{2017}\)
=>\(D=1-\frac17+\frac{1}{7^2}-\frac{1}{7^3}+\cdots-\frac{1}{7^{2017}}\)
=>7D=\(7-1+\frac17-\frac{1}{7^2}+\cdots-\frac{1}{7^{2016}}\)
=>7D+D=\(7-1+\frac17-\frac{1}{7^2}+\cdots-\frac{1}{7^{2016}}+1-\frac17+\frac{1}{7^2}-\frac{1}{7^3}+\cdots-\frac{1}{7^{2017}}\)
=>8D=\(7-\frac{1}{7^{2017}}=\frac{7^{2018}-1}{7^{2017}}\)
=>D=\(\frac{7^{2018}-1}{8\cdot7^{2017}}\)
=>Không có câu nào đúng
