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Giải:
\(\dfrac{2}{3}+\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+\dfrac{2}{99}+\dfrac{2}{143}\)
\(=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+\dfrac{2}{11.13}\)
\(=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}\)
\(=\dfrac{1}{1}-\dfrac{1}{13}\)
\(=\dfrac{12}{13}\)
Chúc em học tốt!
2/3+2/15+2/35+2/63+2/99+2/143
=2(1/1x3+1/3x5+1/5x7+1/7x9+1/9x11+1/11x13)
=2(1-1/3+1/3-1/5+1/5-....+1/13)
=2(1-1/13)
=2.12/13=24/13
Bài làm :
\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}\)
\(=\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}\)
\(=2\times\left(\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+\frac{1}{9\times11}\right)\)
\(=2\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
\(=2\times\left(1-\frac{1}{11}\right)\)
\(=2\times\frac{10}{11}\)
\(=\frac{20}{11}\)
Học tốt nhé
\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}\)
\(=\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}\)
\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)
\(=\frac{1}{1}-\frac{1}{11}=\frac{10}{11}\)
a) 1+2+3+...+99+100
giải
Từ 1 đến 100 có 100 số.Như vậy,số cặp số là:
100:2=50(cặp)
Mỗi cặp số có tổng bằng:
1+100(2+99)(3+98)...=11
Kết quả của phép tính là:
101x50=5050
Đáp số:5050
1 Tính
7/12 - 2/7 + 1/12= (7/12-1/12)+2/7=6/12+2/7=1/2+2/7=7/14+4/14=11/14
12/17-5/17-4/17= 12-5-4/17=3/17
2a, 7/11+3/4+4/11+1/4= (7/11+4/11)+3/4+1/4=11/11+4/4=1+1=2
b)72/99-28/99-14/99= (72-28-14)/99=30/99=10/33
c)69,78+35,97+30,22= (69,78+30,22)+35,97=100+35,97=135,97
d) 83,45-30,98-42,47=83,45-(30,98+42,47)=83,45-73,45=10
câu 1:
\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}\)
\(\hept{\begin{cases}15=3\cdot5\\35=5\cdot7\end{cases}}\\ \hept{\begin{cases}3=3\\63=3^2\cdot7\\99=3^2\cdot11\end{cases}}\)
=>\(\frac{2310}{3465}+\frac{462}{3465}+\frac{198}{3465}+\frac{110}{3465}+\frac{70}{3465}\)
=>\(\frac{2310+462+198+110+70}{3465}\)
=>\(\frac{3150}{3465}\)=\(\frac{10}{11}\)
A = \(\frac{2}{3}+\frac{14}{15}+\frac{34}{35}+\frac{62}{63}+\frac{98}{99}\)
A = ( 1 - 1/3 ) + ( 1 - 1/15 ) + ( 1 - 1/35 ) + ( 1 - 1/63 ) + ( 1 - 1/99 )
A = ( 1 + 1 + 1 + 1 + 1 ) - ( 1/3 + 1/15 + 1/35 + 1/63 + 1/99 )
A = 5 - \(\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right)\)
A = 5 - ( 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 )
A = 5 - ( 1 - 1/11 )
A = 5 - 10/11
A = 45/11
Dấu \(.\)là dấu nhân
\(A=\frac{2}{3}+\frac{14}{15}+\frac{34}{35}+\frac{62}{63}+\frac{98}{99}\)
\(\Rightarrow A=\left(1-\frac{1}{3}\right)+\left(1-\frac{1}{15}\right)+\left(1-\frac{1}{35}\right)+\left(1-\frac{1}{63}\right)+\left(1-\frac{1}{99}\right)\)
\(\Rightarrow A=\left(1+1+1+1+1\right)-\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\right)\)
\(\Rightarrow A=5-\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right)\)
\(\Rightarrow A=5-\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)
\(\Rightarrow A=5-\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
\(\Rightarrow A=5-\frac{1}{2}.\left(1-\frac{1}{11}\right)\)
\(\Rightarrow A=5-\frac{1}{2}.\frac{10}{11}\)
\(\Rightarrow A=5-\frac{5}{11}\)
\(\Rightarrow A=\frac{55}{11}-\frac{5}{11}\)
\(\Rightarrow A=\frac{50}{11}\)
~ Ủng hộ nhé
2/15 + 2/35 + 2/63 + 2/99 + 2/143 + 2/195
\(=2\times\left(\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.11}+\dfrac{1}{11.13}+\dfrac{1}{13.15}\right)\)
= \(2\times\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{15}\right)\)
\(=2\times\left(\dfrac{1}{3}-\dfrac{1}{15}\right)\)
\(=2\times\dfrac{4}{15}\)
\(=\dfrac{8}{15}\)
tính bằng cách nhanh nhất
2/15 + 2/35 + 2/63 + 2/99 + 32/143 + 2/195
Cj' hăm thoát đc đou