3/1.6+3/6.11+3/11.17+.....+3/96.101=?
Giup minh vs
Tính giá trị biểu thức sau:
P = \(\dfrac{3}{1.6}\)+\(\dfrac{3}{6.11}\)+\(\dfrac{3}{11.17}\)+...+\(\dfrac{3}{96.101}\)
P= \(\dfrac{3}{1.6}\)+\(\dfrac{3}{6.11}\)+\(\dfrac{3}{11.17}\)+...+\(\dfrac{3}{96.101}\)
\(\dfrac{5}{3}\).P= \(\dfrac{5}{3}\).(\(\dfrac{3}{1.6}\)+\(\dfrac{3}{6.11}\)+\(\dfrac{3}{11.16}\)+...+\(\dfrac{3}{96.101}\))
\(\dfrac{5}{3}\).P= \(\dfrac{5}{1.6}\)+\(\dfrac{5}{6.11}\)+\(\dfrac{5}{11.16}\)+...+\(\dfrac{5}{96.101}\)
\(\dfrac{5}{3}\).P= \(\dfrac{1}{1}\)-\(\dfrac{1}{6}\)+\(\dfrac{1}{6}\)-\(\dfrac{1}{11}\)+\(\dfrac{1}{11}\)-\(\dfrac{1}{16}\)+...+\(\dfrac{1}{96}\)-\(\dfrac{1}{101}\)
\(\dfrac{5}{3}\).P= \(\dfrac{1}{1}\)-\(\dfrac{1}{101}\)= \(\dfrac{101}{101}\)-\(\dfrac{1}{101}\)=\(\dfrac{100}{101}\)
P= \(\dfrac{100}{101}\):\(\dfrac{5}{3}\)= \(\dfrac{100}{101}\).\(\dfrac{3}{5}\)=\(\dfrac{100.3}{101.5}\)=\(\dfrac{20.3}{101.1}\)=\(\dfrac{60}{101}\)
Vậy P= \(\dfrac{60}{101}\)
E=3/1.6+3/11.6+3/11.17+.......+3/96.101
sửa đề :
\(E=\frac{3}{1\cdot6}+\frac{3}{6\cdot11}+\frac{3}{11\cdot16}+...+\frac{3}{96\cdot101}\)
\(E=3\left(\frac{1}{1\cdot6}+\frac{1}{6\cdot11}+\frac{1}{11\cdot16}+...+\frac{1}{96\cdot101}\right)\)
\(E=3\left[\frac{1}{5}\left(\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+...+\frac{5}{96\cdot101}\right)\right]\)
\(E=3\left[\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{96}-\frac{1}{101}\right)\right]\)
\(E=3\left[\frac{1}{5}\left(1-\frac{1}{101}\right)\right]\)
\(E=3\left[\frac{1}{5}\cdot\frac{100}{101}\right]\)
\(E=3\cdot\frac{20}{101}\)
\(E=\frac{60}{101}\)
tính giá trị biểu thức :A=3/1.6+3/6.11+......................+3/96.101
\(A=\frac{3}{5}.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{96}-\frac{1}{101}\right)\)
\(A=\frac{3}{5}.\left(1-\frac{1}{101}\right)\)
\(A=\frac{3}{5}.\frac{100}{101}\)
\(A=\frac{60}{101}\)
A = 3 - 3/6 + 3/6 - 3/11 + ... + 3/96 - 3/101
A= 3 - 3/101
A= 300/101
A=\(3.\left(\frac{1}{1.6}\right)+\left(\frac{1}{6.11}\right)+...+\left(\frac{1}{96.101}\right)\)
5A=\(3.\left(\frac{5}{1.6}\right)+\left(\frac{5}{6.11}\right)+...+\left(\frac{5}{96.101}\right)\)
5A=3. \(\left(1-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{11}\right)+...+\left(\frac{1}{96}-\frac{1}{101}\right)\)
5A=3.(1-\(\frac{1}{101}\))
5A=3.\(\frac{100}{101}\)
5A=\(\frac{300}{101}\) suy ra A= \(\frac{300}{101}:5\)=\(\frac{60}{101}\)
b=\(\frac{3}{1.6}+\frac{3}{6.11}+\frac{3}{11.16}+..............+\frac{3}{96.101}\)
\(\Leftrightarrow B=\frac{3}{5}.\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{96}-\frac{1}{101}\right)\)
\(\Leftrightarrow B=\frac{3}{5}.\left(\frac{1}{1}-\frac{1}{101}\right)\)
\(\Leftrightarrow B=\frac{3}{5}.\frac{100}{101}\)
\(\Leftrightarrow B=\frac{60}{101}\)
1,B=\(\frac{3}{1.6}+\frac{3}{6.11}+\frac{3}{11.16}+..............+\frac{3}{96.101}\)
Tính tổng\(S=\frac{3}{1.6}+\frac{3}{6.11}+\frac{3}{11.16}+...+\frac{3}{96.101}\)
\(.S=3.\left(\frac{1}{1.6}+\frac{1}{6.11}+...+\frac{1}{96.101}\right)\)
\(\Rightarrow S=3.\frac{1}{5}\left(\frac{1}{1}-\frac{1}{6}+...+\frac{1}{96}-\frac{1}{101}\right)\)
\(\Rightarrow S=\frac{3}{5}.\left(\frac{1}{1}-\frac{1}{101}\right)\)
\(\Rightarrow S=\frac{3}{5}.\left(\frac{100}{101}\right)\)
\(S=\frac{60}{101}\)
\(\frac{100}{101}\)nha
bạn tự tính
tíc mình nha
S=3/1.6+3/6.11+3/11.16+...+3/96.101
=>S=1/1.6+1/6.11+1/11.16+...+1/96.101
S=1-1/6+1/6-1/11+1/11-1/16+...+1/96-1/101
S=1-1/101
S=100/101
Tính tổng: S
\(\frac{3}{1.6}+\frac{3}{6.11}+\frac{3}{11.16}+..+\frac{3}{96.101}\)
\(\frac{3}{1.6}+\frac{3}{6.11}+\frac{3}{11.16}+...+\frac{3}{96.101}\)
\(=3.\frac{1}{5}.\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{96.101}\right)\)
\(=\frac{3}{5}.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{96}-\frac{1}{101}\right)\)
\(=\frac{3}{5}.\left(1-\frac{1}{101}\right)\)
\(=\frac{3}{5}.\frac{100}{101}\)
\(=\frac{60}{101}\)
Tinh gia tri bieu thuc:
A,3/1.6+3/6.11+...+3/96.101. B,1+1/2+1/2^2+1/2^3+....+1/2^2006. C,-1/3+1/3^2+1/3^3+...+1/3^100-1/3^101. D,12-12/7-12/289-12/85 phần 4-4/7-4/289-4/85:3+3/13+3/169+3/91 phần 7+7/13+7/169+7/91
Tính nhanh:
\(\dfrac{5}{1.6}+\dfrac{5}{6.11}+\dfrac{5}{11.16}+....+\dfrac{5}{96.101}\)
Ta có: \(\dfrac{5}{1.6}+\dfrac{5}{6.11}+\dfrac{5}{11.16}+...+\dfrac{5}{96.101}\) \(=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+...+\dfrac{1}{96}-\dfrac{1}{101}\) \(=1-\dfrac{1}{101}\) \(\dfrac{100}{101}\)
\(\dfrac{5}{1.6}+\dfrac{5}{6.11}+\dfrac{5}{11.16}+.....+\dfrac{5}{96.101}\)
\(=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+......+\dfrac{1}{96}-\dfrac{1}{101}\)
\(=1-\dfrac{1}{101}\)
\(=\dfrac{101}{101}-\dfrac{1}{101}\)
\(=\dfrac{101-1}{101}\)
\(=\dfrac{100}{101}\)