a 1/30+2/42+3/56+.....+4/380
b 3-5+7-9+.....+143-145+147
Những câu hỏi liên quan
a 1/30+2/42+3/56+....+4/380
b 3-5+7-9+................+143-145+147
Tính tổng sau: a) 1/2+1/6+1/12+1/20+1/30 b) 1/15+1/35+1/63+1/99+1/143 c) 1/6+1/12+1/20+1/30+1/42+1/56 d) 1/2+1/2^2+1/2^3+1/2^4+1/2^5 e) 1/7+1/7^2+1/7^3+...+1/7^100 f) 1+1/2*(1+2)+1/3*(1+2+3)+1/4*(1+2+3+4)+...+1/200*(1+2+3+..+200) g) (1/2+1)*(1/3+1)*(1/4+1)*..*(1/100+1) h) (1-1/2)*(1-1/3)*(1-1/4)*...*(1-1/2022) Giúp mk vs ạkkk
a) \(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)
=\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}\)
=\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\)
=\(1-\dfrac{1}{6}\)=\(\dfrac{5}{6}\)
b) \(\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}\)
=\(\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.11}+\dfrac{1}{11.13}\)
=\(\dfrac{1.2}{3.5.2}+\dfrac{1.2}{5.7.2}+\dfrac{1.2}{7.9.2}+\dfrac{1.2}{9.11.2}+\dfrac{1.2}{11.13.2}\)
=\(\dfrac{1}{2}\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+\dfrac{2}{11.13}\right)\).
=\(\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}\right)\)
=\(\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{13}\right)\)=\(\dfrac{1}{2}.\dfrac{10}{39}\)=\(\dfrac{5}{39}\).
c) \(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\)
=\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}\)
=\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}\)
=\(1-\dfrac{1}{8}=\dfrac{7}{8}\).
d) \(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}+\dfrac{1}{2^5}\)
=\(\dfrac{2^4}{2^5}+\dfrac{2^3}{2^5}+\dfrac{2^2}{2^5}+\dfrac{2}{2^5}+\dfrac{1}{2^5}\)
=\(\dfrac{2^4+2^3+2^2+2+1}{2^5}\)=\(\dfrac{2^5-1}{2^5}=\dfrac{31}{32}\).
e) \(\dfrac{1}{7}+\dfrac{1}{7^2}+\dfrac{1}{7^3}+...+\dfrac{1}{7^{100}}=\dfrac{7^{99}+7^{98}+7^{97}+...+7+1}{7^{100}}=\dfrac{\dfrac{7^{100}-1}{6}}{7^{100}}=\dfrac{7^{100}-1}{6.7^{100}}\)
Đúng 2
Bình luận (0)
tính thuận tiện
a ( 145 * 99 - 145 ) - ( 143 * 101 - 143 )
b ( 500 * 9 - 250 * 18 ) * ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 +9 )
c ( 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 ) * ( 6 * 8 - 48)
c) \(\left(11+12+13+...+19\right).\left(6.8-48\right)=\left(11+12+13+...+19\right).\left(48-48\right)\)
\(=\left(11+12+13+...+19\right).0\)
\(=0\)
Hok "tuốt" nha^^
b) \(\left(500.9-250.18\right).\left(1+2+3+...+9\right)=\left(250.2.9-250.18\right).\left(1+2+...+9\right)\)
\(=\left(250.18-250.18\right).\left(1+2+3+...+9\right)\)
\(=0.\left(1+2+3+...+9\right)\)
\(=0\)
Hok tốt nha^^ (lần 2)
Tinh hop li:
a.8/9-1/72-1/56-1/42-1/30-1/20-1/12-1/6-1/2
b.(-1/2)-(-3/5)+(-1/9)+1/127-(+7/18)+4/35-(-2/7)
c.3/5+3/11-(-3/7)+(2/97)-1/35-3/4+(-2/7)
A 50
b 97
c 74
k cho mình nhé
Tính
1. A= 1/2+1/6+1/12+/1/20+1/30+1/42+1/56
2. B = 3/2+5/6+7/12+-9/20+11/30-13/42+15/56
A = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56
A = 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8
A = 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8
A = 1 + ( -1/2 + 1/2 ) + ( -1/3 + 1/3 ) + ( -1/4 + 1/4 ) + ( -1/5 + 1/5 ) + ( -1/6 + 1/6 ) + ( -1/7 + 1/7 ) - 1/8
A = 1 + 0 + 0 + 0 + 0 + 0 + 0 - 1/8
A = 1 - 1/8
A = 7/8
* Sửa đề tí nhé
B = 3/2 - 5/6 + 7/12 - 9/20 + 11/30 - 13/42 + 15/56
B = 3/1.2 - 5/2.3 + 7/3.4 - 9/4.5 + 11/5.6 - 13/6.7 + 15/7.8
B = 3 - 3/2 - 5/2 - ( -5/3 ) + 7/3 - 7/4 - 9/4 - ( -9/5 ) + 11/5 - 11/6 - 13/6 - ( -13/7 ) + 15/7 - 15/8
B = 3 - 3/2 - 5/2 + 5/3 + 7/3 - 7/4 - 9/4 + 9/5 + 11/5 - 11/6 - 13/6 + 13/7 + 15/7 - 15/8
B = 3 + ( -3/2 - 5/2 ) + ( 5/3 + 7/3 ) + ( -7/4 - 9/4 ) + ( 9/5 + 11/5 ) + ( -11/6 - 13/6 ) + ( 13/7 + 15/7 ) - 15/8
B = 3 + -4 + 4 + -4 + 4 + -4 + 4 - 15/8
B = 3 + 0 + 0 + 0 - 15/8
B = 3 - 15/8
B = 9/8
Tính hợp lý
a) 0.5+1/3+0.4+5/4+1/6-4/35
b) 8/9-1/72-1/56-1/42-1/30-1/20-1/12-1/6-1/2
c) 1/3*-4/5+1/3+-6/5
d)3/7*9/26-1/14*1/13
e) (-3/4+2/5):3/7+(3/5+-1/4):3/7
a .(18 – 9 x 2) x (2 + 4 + 6 + 8 + 10)b.(7 x 8 – 56 ) : (2 + 4 + 6 + 8 + 112)c. (2 + 125 + 6 + 145 + 112) x (42 – 6 x 7)d.(12 x 6 – 12 x 4 – 12 x 2) x ( 347 + 125)e(a x 7 + a x 8 – a x 15) : (1 + 2 + 3 + ........ + 10)f.58 – 58 x (6 + 54 – 60)g.32 + 63 x a x ( a x 1 – a : 1) + 32 x 8 + 32h.(1 + 2 + 3 + 4 + .... + 9) x (21 x 5 – 21 – 4 x21)i.(9 x 7 + 8 x 9 – 15 x 9) : (1 + 3 + 5 + 7 + ........+ 17 + 19)k.(2 + 4 + 6 + 8 + ... + 20) x (56 x 3 – 72 : 9 x 21)
Đọc tiếp
a .(18 – 9 x 2) x (2 + 4 + 6 + 8 + 10)
b.(7 x 8 – 56 ) : (2 + 4 + 6 + 8 + 112)
c. (2 + 125 + 6 + 145 + 112) x (42 – 6 x 7)
d.(12 x 6 – 12 x 4 – 12 x 2) x ( 347 + 125)
e(a x 7 + a x 8 – a x 15) : (1 + 2 + 3 + ........ + 10)
f.58 – 58 x (6 + 54 – 60)
g.32 + 63 x a x ( a x 1 – a : 1) + 32 x 8 + 32
h.(1 + 2 + 3 + 4 + .... + 9) x (21 x 5 – 21 – 4 x21)
i.(9 x 7 + 8 x 9 – 15 x 9) : (1 + 3 + 5 + 7 + ........+ 17 + 19)
k.(2 + 4 + 6 + 8 + ... + 20) x (56 x 3 – 72 : 9 x 21)
1.(18 - 18) x (2 + 8) + ( 4 + 6) + 10 = 30
có rút gọn phân số 35/6 về phân số đc ko ? Nếu có thì mn rút gọn cho mik nhé !
Ai xong tr tui k cho
a) N = 1/2 + 1/6+ 1/12 + 1/20 + 1/30 +1/42 + 1/56 + 1/72 +1/90
b) 5/8 + 2/9 -2/5 + 3/8 + 4/9 + 1/3 - 3/5 =
c) 4 1/5 + 5 1/3 - 2 2/3 x 3 1/5 + 9/25 : 9/20 =