15/6+15/66+15/176+...+15/1116
tính
3 x 5/11
16/64 x 15/24
1/6 : 1/5
7/12 : 1/4
\(3\times\dfrac{5}{11}=\dfrac{15}{11}\)
\(\dfrac{16}{64}\times\dfrac{15}{24}=\dfrac{5}{32}\)
\(\dfrac{1}{6}:\dfrac{1}{5}=\dfrac{5}{6}\)
\(\dfrac{7}{12}:\dfrac{1}{4}=\dfrac{7}{3}\)
Tính tổng 100 s/h đầu tiên của dãy
A= 2/3; 2/15; 2/35; 2/63; ...
B= 1/6; 1/66; 1/176; 1/336; ...
C= 3; 3/2; 3/2^2; 3/2^3; ...
Tính giá trị biểu thức : 15 + 6 6 - 15 - 6 6
A. 2 6
B. − 2 6
C. 6
D. 0
Giá trị của biểu thức 15 - 6 6 + 15 + 6 6 bằng:
A.12 6
B.6
C. 30
D.3
Đáp án là B
15 - 6 6 + 15 + 6 6
= 9 - 6 6 + 6 + 9 + 6 6 + 6 = 3 - 6 2 + 3 + 6 2
= |3 - 6 | + |3 + 6 |
= 3 - 6 + 3 + 6
= 6
Giá trị của biểu thức 15 - 6 6 + 15 + 6 6 bằng:
A.6
B.12 6
C. 30
D.3
\(15(-176)+15\times76\)
\(15.\left(-176\right)+15.76\)
\(=15.76-15.176\)
\(=15.\left(76-176\right)\)
\(=-15.100=-1500\)
15( - 176) + 15 x 76
= 15[( -176) + 76]
=15(-100)
= -1500
hok good
15.(-176)+15.76
15.[(-176)+76]
15.-100
-1500
2-5/3+7/6-9/10+11/15-13/21+15/28-17/36+19/45-21/55+23/66
so sánh A = 1/10 + 1/15 + 1/21 + ... +1/66 VÀ B = 1/6 + 1/10 + 1/15 +... +1/55
\(A=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{66}\)
\(\frac{A}{2}=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{132}\)
\(\frac{A}{2}=\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+...+\frac{1}{11\cdot12}\)
\(\frac{A}{2}=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{11}-\frac{1}{12}\)
\(\frac{A}{2}=\frac{1}{4}-\frac{1}{12}\)
\(\Rightarrow A=\frac{2}{4}-\frac{2}{12}=\frac{16}{48}\)
\(B=\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{55}\)
\(\frac{B}{2}=\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{110}\)
\(\frac{B}{2}=\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...+\frac{1}{10\cdot11}\)
\(\frac{B}{2}=\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\)
\(\frac{B}{2}=\frac{1}{3}-\frac{1}{11}\)
\(\Rightarrow B=\frac{2}{3}-\frac{2}{11}=\frac{16}{33}\)
Mà \(\frac{16}{48}< \frac{16}{33}\Rightarrow A< B\)
Vậy : A < B
A=1/3+1/6+1/10+1/15+...+1/66
B= 2/15+2/35+2/63+..+2/399
\(B=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)
\(B=\frac{2}{3×5}+\frac{2}{5×7}+\frac{2}{7×9}+...+\frac{2}{19×21}\)
\(B=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{19}-\frac{1}{21}\)
\(B=\frac{1}{3}-\frac{1}{21}\)
\(B=\frac{2}{7}\)
A=\(\frac{1}{3}\)+\(\frac{1}{6}\)+\(\frac{1}{10}\)+\(\frac{1}{15}\)+...+\(\frac{1}{66}\)
A=\(\frac{1}{1\cdot3}\) +\(\frac{1}{2\cdot3}\) +\(\frac{1}{2\cdot5}\)+...+\(\frac{1}{6\cdot11}\)
A=\(\frac{1}{1}-\frac{1}{3}+\frac{1}{2}-\frac{1}{3}+\frac{1}{2}-\frac{1}{5}+...+\frac{1}{6}-\frac{1}{11}\)
A=\(\frac{1}{1}-\frac{1}{11}\)
=>A=\(\frac{10}{11}\)
B=\(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)
2B=\(\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{19\cdot21}\)
2B=\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)
2B=\(\frac{1}{3}-\frac{1}{21}\)
2B=\(\frac{2}{7}\)
B=\(\frac{2}{7}:2\)
=>B=\(\frac{1}{7}\)