Tính nhanh
B = \(\frac{1}{1.2}+\frac{2}{1.7}+\frac{3}{2.7}+\frac{2}{1.14}+\frac{1}{3.14}+\frac{4}{3.19}+\frac{1}{4.19}\)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(B=-\frac{1}{1.2}-\frac{1}{2.3}-\frac{1}{3.4}-...-\frac{1}{98.99}-\frac{1}{99.100}\\
=-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)\\
=-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\\
=-\left(1-\frac{1}{100}\right)=\frac{-99}{100}\)
Đặt \(B=\frac{1}{1.2}+\frac{5}{2.7}+\frac{8}{7.15}+\frac{13}{15.28}+\frac{21}{28.49}+\frac{32}{49.81}\)
\(\Rightarrow B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}+\frac{1}{28}-\frac{1}{49}+\frac{1}{49}-\frac{1}{81}\)
\(\Rightarrow B=1-\frac{1}{81}\)
\(\Rightarrow B=\frac{80}{81}\)
1/2.17+1/3.18+1/4.19+...+1/1990.2005=1/15.(15/2.17+15/3.18+...+15/1990.2005)=1/15.(1/2-1/2005).
phan con lai pan tu tinh
1/2.17+1/3.18+1/4.19+...+1/1990.2005=1/15.(15/2.17+15/3.18+...+15/1990.2005)=1/15.(1/2-1/2005)=1/15.2003/4010=2003/60150