a,2/5.7 + 2/7.9 + 2/9.11 + ... + 2/53.55
b,1/2 .1/3 +1/4 . 1/5 + ... + 1/8 . 1/9
c,(1+1/2)(1+1/3)(1=1/4).....(1+1/99)
1. Tính một cách hợp lí nhất:
a) 1/5.7 + 1/7.9 + 1/9.11 + ... + 1/97. 99
b) 1/5 + 1/52 + ... + 1/52017
c) 1/10 + 1/15 + 1/21 + ... + 1/120
d)(1/2 + 1)x(1/3 + 1)x(1/4 + 1)x ... (1/99 + 1)
e) 3/22 x 8/32 x 15/42 x ... x (1/99 + 1)
Mọi người giúp mik vs nhé. Mik đang cần gấp! Ai nhanh mik tick cho.
1. Tính:
D = 3/5.7 + 3/7.9 + 3/9.11 + ... + 3/53.55
2. Tìm x sao cho:
A = x+2/x-5 là số nguyên dương
3. Chứng tỏ rằng:
S = 1/2 + 1/2^2 + 1/2^3 + ... + 1/2^20 nhỏ hơn 1
A = 1/10 + 1/11 + 1/12 + ... + 1/99 + 1/100 lớn hơn 1
Giúp mình với. Hu hu
1:
Ta có: \(D=\dfrac{3}{5\cdot7}+\dfrac{3}{7\cdot9}+\dfrac{3}{9\cdot11}+...+\dfrac{3}{53\cdot55}\)
\(=\dfrac{3}{2}\left(\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+\dfrac{2}{9\cdot11}+...+\dfrac{2}{53\cdot55}\right)\)
\(=\dfrac{3}{2}\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+...+\dfrac{1}{53}-\dfrac{1}{55}\right)\)
\(=\dfrac{3}{2}\left(\dfrac{1}{5}-\dfrac{1}{55}\right)\)
\(=\dfrac{3}{2}\left(\dfrac{11}{55}-\dfrac{1}{55}\right)\)
\(=\dfrac{3}{2}\cdot\dfrac{2}{11}=\dfrac{3}{11}\)
2) Để A là số nguyên dương thì
\(\left\{{}\begin{matrix}x+2⋮x-5\\x-5>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-5+7⋮x-5\\x>5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}7⋮x-5\\x>5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-5\inƯ\left(7\right)\\x>5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-5\in\left\{1;-1;7;-7\right\}\\x>5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\in\left\{6;4;12;-2\right\}\\x>5\end{matrix}\right.\)
\(\Leftrightarrow x\in\left\{6;12\right\}\)
Giải:
1)D=3/5.7+3/7.9+3/9.11+...+3/53.55
D=3/2.(2/5.7+2/7.9+2/9.11+...+2/53.55)
D=3/2.(1/5-1/7+1/7-1/9+1/9-1/11+...+1/53-1/55)
D=3/2.(1/5-1/55)
D=3/2.2/11
D=3/11
1)Tính:
P= 2/3.5+2/5.7+2/7.9+2/9.11+2/11.13+2/13.15
2) Thực hiện phép tính:
a) 0,2:1/3/5+80%
b) 0,5:5/4-2/1/5
1) P = 2/3.5 + 2/5.7 + 2/7.9 + 2/9.11 + 2/11.13 + 2/13.15
P= (1/3-1/5) + (1/5-1/7) + (1/7-1/9) + (1/9-1/11) + (1/11-1/13) + (1/13-1/15)
P=1/3-1/15= 4/15
2) a/ 0,2:1+3/5+80%
= 2/10:8/5+8/10
= 2/10.5/8+8/10
= 1/8 + 4/5 = 5/40 + 32/40 = 37/40
b/ 0,5:5/4-2+1/5
= 5/10:5/4-11/5
= 5/10.4/5-11/5
=2/5-11/5 = -9/5
( 1/1.3+1/3.5+1/5.7+1/7.9+1/9.11). X = 2/3
\(\text{Ta có:}\) \(\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right).x=\frac{2}{3}\)
\(\Leftrightarrow2.\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right).x=\frac{2}{3}.2\)
\(\Leftrightarrow\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right).x=\frac{4}{3}\)
\(\Leftrightarrow\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{9}-\frac{1}{11}\right).x=\frac{4}{3}\)
\(\Leftrightarrow\left(1-\frac{1}{11}\right)x=\frac{4}{3}\)
\(\Leftrightarrow\frac{10}{11}x=\frac{4}{3}\)
\(\Leftrightarrow x=\frac{4}{3}:\frac{10}{11}=\frac{22}{15}\)
Tính nhanh:
1. \(\dfrac{1}{15}\)+ \(\dfrac{1}{35}\)+ \(\dfrac{1}{63}\)+ \(\dfrac{1}{99}\)+ \(\dfrac{1}{143}\)
2. \(\dfrac{5}{1.3}\)+ \(\dfrac{5}{1.5}\)+ \(\dfrac{5}{5.7}\)+ \(\dfrac{5}{7.9}\)+ \(\dfrac{5}{9.11}\)
1: \(=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{11}-\dfrac{1}{13}\right)\)
=1/2*10/39
=5/39
2: \(=\dfrac{5}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{11}\right)=\dfrac{5}{2}\cdot\dfrac{10}{11}=\dfrac{50}{22}=\dfrac{25}{11}\)
Tìm y : ( 1/1.3 + 1/3.5 + 1/5.7 + 1/7.9 + 1/9.11 ) .y = 2/3.
( \(\frac{1}{1x3}\)+ \(\frac{1}{3x5}\)+....+\(\frac{1}{9x11}\)) x \(y\) = \(\frac{2}{3}\)
( \(\frac{2}{1x3}\)+ \(\frac{2}{3x5}\)+...+\(\frac{2}{9x11}\)) x \(y\) = \(\frac{4}{3}\) (nhân 2 vế lên với 2)
(1 - \(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)- ...+ \(\frac{1}{9}\)- \(\frac{1}{11}\)) x \(y\)= \(\frac{4}{3}\)
( 1 - \(\frac{1}{11}\)) x \(y\)=\(\frac{4}{3}\)
\(\frac{10}{11}\) x \(y\) =\(\frac{4}{3}\)
\(y\) = \(\frac{4}{3}\): \(\frac{10}{11}\)
\(y\) = \(\frac{4}{3}\)x \(\frac{11}{10}\)
\(y\) =\(\frac{22}{15}\)
kết quả đúng nhưng mình ko hiểu bạn có thể giáng lại ko ?
1, 1/7 + 1/91 + 1/247 + 1/475 + 1/775 + 1/1147
2, 1/6 + 5/6.7 + 1/7.8 + 5/8.9 + ... + 1/24.25
3, 22/5.7 + 22/7.9 + 22/9.11 + ... + 22/39.41
1,tính
a, (-5/24+0,75+7/12):(hỗn sô -2ba phan 8)
b, -3/8.2/5+-3/5.9/8_-3/8.6/5
c, 2/5.7+2/7.9+2/9.11+....+2/59.61
2, tìm x
2/3.x+1/2.x-x+4
3, a, so sánh
A=17^18+1/17^19+1 ; B=17^17+1/17^18+1
b, tìm các số nguyên n để
A=n+1/n-2 là số nguyên
tìm x, biết
\(\frac{1}{2}-\frac{1}{1.3}-\frac{1}{3.5}-\frac{1}{5.7}-\frac{1}{7.9}-\frac{1}{9.11}=\frac{4}{5}-x\)
\(\frac{1}{2}-\frac{1}{1.3}-\frac{1}{3.5}-\frac{1}{5.7}-\frac{1}{7.9}-\frac{1}{9.11}=\frac{4}{5}-x\)
<=> \(2.\frac{1}{2}-\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)=\frac{8}{5}-2x\)
<=> \(1-\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}\right)=\frac{8}{5}-2x\)
<=> \(1-\left(1-\frac{1}{11}\right)-\frac{8}{5}=-2x\)
<=> \(-\frac{83}{55}=-2x\)
<=> \(x=\frac{83}{110}\)