Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{1}{26.31}\)
\(=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\)
\(=1+\left(-\frac{1}{6}+\frac{1}{6}\right)+\left(-\frac{1}{11}+\frac{1}{11}\right)+...+\left(-\frac{1}{26}+\frac{1}{26}\right)-\frac{1}{31}\)
\(=1-\frac{1}{31}=\frac{31-1}{31}\)
\(=\frac{30}{31}\)
Vậy \(A=\frac{30}{31}\)
\(A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}\)
\(\Rightarrow A=\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\)
\(\Rightarrow A=\frac{1}{1}-\frac{1}{31}\)
\(\Rightarrow A=\frac{30}{31}\)
\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}\)
\(=5^2\left(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+\frac{1}{21.26}\right)\)
\(=25.\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{21}-\frac{1}{26}\right)\)
\(=5\left(1-\frac{1}{26}\right)\)
\(=5.\frac{25}{26}\)
\(=\frac{125}{26}\)
\(\Rightarrow A=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+.....+\frac{1}{26}-\frac{1}{31}\)
\(\Rightarrow A=1-\frac{1}{31}\)
\(\Rightarrow A=\frac{30}{31}\)
\(A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}\)
\(=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\)
\(=1+\left(-\frac{1}{6}+\frac{1}{6}\right)+\left(-\frac{1}{11}+\frac{1}{11}\right)+...+\left(-\frac{1}{26}+\frac{1}{26}\right)-\frac{1}{31}\)
\(=1-\frac{1}{31}=\frac{31-1}{31}=\frac{30}{31}\)
\(\text{Vậy }A=\frac{30}{31}\).
\(S=\frac{5^2}{1\cdot6}+\frac{5^2}{6\cdot11}+\frac{5^2}{11\cdot16}+\frac{5^2}{16\cdot21}+\frac{5^2}{21\cdot26}\)
\(S=\frac{25}{1\cdot6}+\frac{25}{6\cdot11}+\frac{25}{11\cdot16}+\frac{25}{16\cdot21}+\frac{25}{21\cdot26}\)
\(S=5\left[\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+\frac{5}{16\cdot21}+\frac{5}{21\cdot26}\right]\)
\(S=5\left[1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{21}-\frac{1}{26}\right]\)
\(S=5\left[1-\frac{1}{26}\right]=5\cdot\frac{25}{26}=\frac{125}{26}\)
Bài làm
S = \(\frac{5^2}{1.6}\)+ \(\frac{5^2}{6.11}\)+ \(\frac{5^2}{11.16}\)+ \(\frac{5^2}{16.21}\)+\(\frac{5^2}{21.26}\)
S : 5 = \(\frac{5}{1.6}\)+ \(\frac{5}{6.11}\)+ \(\frac{5}{11.16}\) + \(\frac{5}{16.21}\) + \(\frac{5}{21.26}\)
S : 5 = 1 - \(\frac{1}{6}\)+ \(\frac{1}{6}\)- \(\frac{1}{11}\) + \(\frac{1}{11}\)- \(\frac{1}{16}\)+ \(\frac{1}{16}\)- \(\frac{1}{21}\)+ \(\frac{1}{21}\)- \(\frac{1}{26}\)
S : 5 = 1 - \(\frac{1}{26}\)
S : 5 = \(\frac{25}{26}\)
S = \(\frac{125}{26}\)
\(\frac{1}{1.6}+\frac{1}{6.11}+...+\frac{1}{96.101}\)
\(=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{96}-\frac{1}{101}\)
\(=1-\frac{1}{101}\)
\(=\frac{100}{101}\)
đặt biểu thức là A
5A=(1/1x6+1/6x11+...+1/96x101)x5=5/1x6+5/6x11+...+5/96x101
5A=6-1/1x6+11-6/6x11+...+101-96/96x101
5A=6/1x6-1/1x6+11/6x11-6/6x11+...+101/96x101-96/96x101
5A=1-1/6+1/6-1/11+...+1/96-1/101(sau khi rút gọn các phân số)
5A=1-1/101(còn lại sau khi trừ)
5A=100/101
A=100/101:5=20/101
