Tính
A= 10/7.12 + 10/12.17 + 10/17.22 + .... + 10/502.507
B= 1/6.10 + 1/10.14 + 1/14.18 +.... + 1/ 402.406
Nhanhh nhaaa iuuu iuuu
Tính:A=1/7.12+1/12.17+1/17.22+...+1/52.57
B=10/8.13+10/13.18+10/18.23+...+10/253.258
\(A=\frac{1}{7\cdot12}+\frac{1}{12\cdot17}+\frac{1}{17\cdot22}+...+\frac{1}{52\cdot57}\)
\(A=\frac{1}{5}\left(\frac{5}{7\cdot12}+\frac{5}{12\cdot17}+\frac{5}{17\cdot22}+...+\frac{5}{52\cdot57}\right)\)
\(A=\frac{1}{5}\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+...+\frac{1}{52}-\frac{1}{57}\right)\)
\(A=\frac{1}{5}\left(\frac{1}{7}-\frac{1}{57}\right)=\frac{1}{5}\cdot\frac{50}{399}=\frac{10}{399}\)
\(B=\frac{10}{8\cdot13}+\frac{10}{13\cdot18}+\frac{10}{18\cdot23}+...+\frac{10}{253\cdot258}\)
\(B=\frac{10}{5}\left(\frac{5}{8\cdot13}+\frac{5}{13\cdot18}+\frac{5}{18\cdot23}+...+\frac{5}{253\cdot258}\right)\)
\(B=2\left(\frac{1}{8}-\frac{1}{13}+\frac{1}{13}-\frac{1}{18}+...+\frac{1}{253}-\frac{1}{258}\right)\)
\(B=2\left(\frac{1}{8}-\frac{1}{258}\right)=2\cdot\frac{125}{1032}=\frac{125}{516}\)
*Cái đây giải thích hơi bị " khó hiểu " :
Chỗ mẫu (12 - 7) = (17 - 12) = ... = (57 - 52) = 5
Tử là 1 , mẫu là 5 nên tử/mẫu = 1/5
Hay \(\frac{1}{5}\left(\frac{5}{7\cdot12}+\frac{5}{12\cdot17}+...+\frac{5}{52\cdot57}\right)\)
Còn bạn Trương Bùi Linh thì :
Mẫu = (13 - 8) = (18 - 13) = (23 - 18) = ... = 5
Tử là 10,mẫu là 5 => tử / mẫu = 10/5 = 2
tính:
B= 10/7.12+10/12.17+10/17.22+.......+10/502.507
\(B=2\left(\frac{5}{7.12}+\frac{5}{12.17}+...+\frac{5}{502.507}\right)\)
\(B=2\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+...+\frac{1}{502}-\frac{1}{507}\right)\)
\(B=2\left(\frac{1}{7}-\frac{1}{507}\right)\)
\(B=2\times\frac{500}{3549}\)
\(B=\frac{1000}{3549}\)
\(B=\frac{10}{7.12}+\frac{10}{12.17}+\frac{10}{17.22}+......+\frac{10}{502.507}\)
\(B=\frac{10}{5}.\left(\frac{5}{7.12}+\frac{5}{12.17}+\frac{5}{17.22}+........+\frac{5}{502.507}\right)\)
\(B=\frac{10}{5}.\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+\frac{1}{17}-\frac{1}{22}+.....+\frac{1}{502}-\frac{1}{507}\right)\)
\(B=\frac{10}{5}.\left(\frac{1}{7}-\frac{1}{507}\right)=2.\frac{500}{3549}=\frac{1000}{3549}\)
K=10/7.12+10/12.17+10/17.22+...+10/502.507
Ai nhanh mk tik
\(K=\frac{10}{7.12}+\frac{10}{12.17}+\frac{10}{17.22}+...+\frac{10}{502.507}\)
\(\Leftrightarrow K=\frac{10}{5}\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+\frac{1}{17}-\frac{1}{22}+...+\frac{1}{502}-\frac{1}{507}\right)\)
\(\Leftrightarrow K=2\left(\frac{1}{7}-\frac{1}{507}\right)\)
\(\Leftrightarrow K=2\cdot\frac{500}{3549}\)
\(\Leftrightarrow K=\frac{1000}{3549}\)
5xK=5/7.12+5/12.17+..............+5/502.507
5xK=(1/7-1/12)+(1/12-1/17)+........+(1/502-1/507)
5xK=1/7-1/507
5xK=500/3549
K =500/3549:5
K =100/3549
\(B=\frac{10}{7.12}+\frac{10}{12.17}+\frac{10}{17.22}+...+\frac{10}{2017.2022}\)
\(=2\left(\frac{5}{7.12}+\frac{5}{12.17}+\frac{5}{17.22}+...+\frac{5}{2017.2022}\right)\)
\(=2\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+...+\frac{1}{2017}-\frac{1}{2022}\right)\)
\(=2\left(\frac{1}{7}-\frac{1}{2022}\right)=\frac{2015}{7077}\)
\(B=\frac{10}{7.12}+\frac{10}{12.17}+\frac{10}{17.22}+...+\frac{10}{2017.2022}\)
\(\Rightarrow B=2.\left(\frac{5}{7.12}+\frac{5}{12.17}+\frac{5}{17.22}+...+\frac{5}{2017.2022}\right)\)
\(\Rightarrow B=2.\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+\frac{1}{17}-\frac{1}{22}+...+\frac{1}{2017}-\frac{1}{2022}\right)\)
\(\Rightarrow B=2.\left(\frac{1}{7}-\frac{1}{2022}\right)\)
\(\Rightarrow B=2.\frac{2015}{14154}\)
\(\Rightarrow B=\frac{2015}{7077}.\)
Vậy \(B=\frac{2015}{7077}.\)
Chúc bạn học tốt!
Tính : \(N=2015+\frac{10}{2.7}+\frac{10}{7.12}+\frac{10}{12.17}+\frac{10.}{17.22}\)
\(N=2015+\frac{10}{2.7}+\frac{10}{7.12}+\frac{10}{12.17}+\frac{10}{17.22}\)
\(=2\left(1007,5+\frac{5}{2.7}+\frac{5}{7.12}+\frac{5}{12.17}+\frac{5}{17.22}\right)\)
\(=2\left(1007,5+\frac{7-2}{2.7}+\frac{12-7}{7.12}+\frac{17-12}{12.17}+\frac{22-17}{17.22}\right)\)
\(=2\left(1007,5+\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+\frac{1}{17}-\frac{1}{22}\right)\)
\(=2\left(1007,5+\frac{1}{2}-\frac{1}{22}\right)\)
\(=2015+1-\frac{1}{11}\)
\(=\frac{22175}{11}\)
N = \(2015+\frac{10}{2,7}+\frac{10}{7,12}+\frac{10}{12,17}+\frac{10}{17,22}=2021.510611\)
\(N=2015+\frac{10}{2\cdot7}+\frac{10}{7\cdot12}+\frac{10}{12\cdot17}+\frac{10}{17\cdot22}=2015+2\left(\frac{5}{2\cdot7}+\frac{5}{7\cdot12}+\frac{5}{12\cdot17}+\frac{5}{17\cdot22}\right)\)\(=2015+2\left(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+\frac{1}{17}-\frac{1}{22}\right)\)
\(=2015+2\left[\left(\frac{1}{2}-\frac{1}{22}\right)+\left(\frac{1}{7}-\frac{1}{7}\right)+...+\left(\frac{1}{17}-\frac{1}{17}\right)\right]\)
\(=2015+2\left[\left(\frac{11}{22}-\frac{1}{22}\right)+0+...+0\right]=2015+2\cdot\frac{10}{22}=2015+\frac{10}{11}\)
xong rồi đó, cái còn lại thì bạn quy đồng rồi cộng nha
mk cũng ko chắc do tính nhẩm
tính nhanh :
C = \(\frac{10}{7.12}+\frac{10}{12.17}+\frac{10}{17.22}+....+\frac{10}{502.507}\)
\(\Rightarrow C=\frac{10}{5}\left(\frac{1}{7.12}+\frac{1}{12.17}+\frac{1}{17.22}+...+\frac{1}{502.507}\right)\)
\(\Rightarrow C=2.\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+....+\frac{1}{507}-\frac{1}{507}\right)\)
\(\Rightarrow C=2.\left(\frac{1}{7}-\frac{1}{507}\right)=2.\frac{1}{7}-2.\frac{1}{507}=\frac{2}{7}-\frac{2}{507}\)
Tính nhanh:
a) \(A=\frac{3}{5.8}\)+ \(\frac{3}{8.11}\)+ \(\frac{3}{11.14}\)+ ... + \(\frac{3}{2006.2009}\)
b) \(B=\frac{1}{6.10}\)+ \(\frac{1}{10.14}\)+ \(\frac{1}{14.18}\)+...+ \(\frac{1}{402.406}\)
c) \(C=\frac{10}{7.12}\)+\(\frac{10}{12.17}\)+\(\frac{10}{17.22}\)+...+\(\frac{10}{502.507}\)
d) \(D=\frac{4}{8.13}\)+\(\frac{4}{13.18}\)+\(\frac{4}{18.23}\)+...+\(\frac{4}{253.258}\)
Nếu ai có giải dùm mình thì giải từng phần nhưng đừng chỉ ghi kết quả nhé~
a,\(\frac{2004}{10045}\)
b,\(\frac{25}{609}\)
c,\(\frac{1000}{3549}\)
d,\(\frac{25}{258}\)
A) \(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+.....+\frac{1}{2006}-\frac{1}{2009}=\frac{1}{5}-\frac{1}{2009}=\frac{2004}{10045}\)các câu sau không theo quy luật bạn phải quy đồng mình đã giải xong câu a) rồi đấy bạn hãy vận dụng nó để giải các câu còn lại nên nhớ câu a) theo quy luật còn các câu còn lại không theo quy luật nên ta quy đồng không phải là mình không biết làm đâu => tại mình mỏi tay quá
C = \(\dfrac{10}{7.12}+\dfrac{10}{12.17}+\dfrac{10}{17.22}+....+\dfrac{10}{502.507}\)
D = \(\dfrac{3}{5.8}+\dfrac{3}{8.11}+\dfrac{3}{11.14}+....+\dfrac{3}{2006.2009}\)
tính giúp mk với
D = \(\dfrac{3}{5.8}+\dfrac{3}{8.11}+\dfrac{3}{11.14}+...+\dfrac{3}{2006.2009}\)
= \(\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+...+\dfrac{1}{2006}-\dfrac{1}{2009}\)
= \(\dfrac{1}{5}-\dfrac{1}{9}=\dfrac{2004}{10045}\)
C = \(\dfrac{10}{7.12}+\dfrac{10}{12.17}+\dfrac{10}{17.22}+...+\dfrac{10}{502.507}\)
= \(\dfrac{10}{5}\left(\dfrac{5}{7.12}+\dfrac{5}{12.17}+\dfrac{5}{17.22}+...+\dfrac{5}{502.507}\right)\)
= \(\dfrac{10}{5}\left(\dfrac{1}{7}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{22}+....+\dfrac{1}{502}-\dfrac{1}{507}\right)\)
= \(\dfrac{10}{5}\left(\dfrac{1}{5}-\dfrac{1}{507}\right)\)
= \(\dfrac{10}{5}.\dfrac{502}{2535}\)
= \(\dfrac{1000}{3549}\)
Tính
a) A= 1/2.9 + 1/9.7 + 1/7.19 +....+ 1/252.509
b) B= 1/10.9 + 1/18.13 + 1/26.17+.... + 1/802.405
Nhanh nhaaa iuuu
a)Ta có:
A= 1/2.9 + 1/9.7 +...+1/252.509
= 2/5.(5/4.9 + 5/9.14 + 5/14.19 +...+ 1/504.509)
= 2/5.(1/4 - 1/9 + 1/9 - 1/14 + 1/14 - 1/19 +...+ 1/504 - 1/509)
= 2/5.(1/4 - 1/509)
= 101/1018
Vậy A = 101/1018
b)Ta có:
B= 1/10.9 +1/18.13 + 1/26.17 +...+ 1/802.405)
= 1/4.(8/10.18 + 8/18.26 + 8/26.34 +...+ 8/802.810)
= 1/4.(1/10 - 1/18 + 1/18 - 1/26 + 1/26 - 1/34 +...+ 1/802 - 1/810)
= 1/4.(1/10 - 1/810)
= 2/81
Vậy B= 2/81
Tk mình nha!!!