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
Câu 29: \(A=1+3+3^2+\cdots+3^{100}\)
=>\(3A=3+3^2+3^3+\cdots+3^{101}\)
=>3A-A=\(3+3^2+3^3+\cdots+3^{101}-1-3-3^2-\cdots-3^{100}\)
=>\(2A=3^{101}-1\)
=>\(2A+1=3^{101}\)
=>\(3^{n}=3^{101}\)
=>n=101
Câu 28: B
Câu 27: \(G=\frac35+\frac{3}{5^4}+\frac{3}{5^7}+\cdots+\frac{3}{5^{100}}\)
=>\(5^3\cdot G=3\cdot5^2+\frac35+\frac{3}{5^4}+\cdots+\frac{3}{5^{97}}\)
=>125G-G=\(3\cdot5^2+\frac35+\frac{3}{5^4}+\cdots+\frac{3}{5^{97}}-\frac35-\frac{3}{5^4}-\cdots-\frac{3}{5^{100}}\)
=>124G=\(75-\frac{3}{5^{100}}=\frac{75\cdot5^{100}-3}{5^{100}}\)
=>\(G=\frac{75\cdot5^{100}-3}{124\cdot5^{100}}\)
