b) 2047/1024
Còn câu a bạn có chép đúng đề ko đấy?
a) \(A=1.2+2.3+3.4+...+98.97\)
\(\Rightarrow A=1.2+2.3+3.4+...+97.98\)
\(\Rightarrow3A=1.2.3+2.3.3+3.4.3+...+97.98.3\)
\(\Rightarrow3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+97.98.\left(99-96\right)\)
\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+...+97.98.99-96.97.98\)
\(\Rightarrow3A=97.98.99\)
\(\Rightarrow A=97.98.33\)
b) \(B=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\)
\(\Rightarrow B=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\)
\(\Rightarrow2B=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)
\(\Rightarrow2B-B=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}-1-\frac{1}{2}-\frac{1}{2^2}-...-\frac{1}{2^{10}}\)
\(\Rightarrow B=2-\frac{1}{2^{10}}\)
\(\Rightarrow B=\frac{2048}{1024}-\frac{1}{1024}\)
\(\Rightarrow B=\frac{2047}{1024}\)
