Tính bằng cách nhanh nhất 1/2+1/6+1/12+1/20
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
MT
1
IW
13 tháng 9 2016
Đặt \(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+......+\frac{1}{56}\)
\(\Rightarrow A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+........+\frac{1}{7.8}\)
\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{7}-\frac{1}{8}\)
\(\Rightarrow A=1-\frac{1}{8}\)
\(\Rightarrow A=\frac{7}{8}\)
BT
30 tháng 3 2018
a/ \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}=\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}=\)
= 1-1/8 = 7/8
b/ = (17/9+1/9)+(19/13+7/13)+(14/6+10/6) = 18/9 + 26/13 + 24/6 = 2+2+4 = 8
D
10 tháng 1 2023
\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+....+\dfrac{1}{110}\)
\(=\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+....+\dfrac{1}{10\times11}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+....+\dfrac{1}{10}-\dfrac{1}{11}\)
\(=1-\dfrac{1}{11}=\dfrac{10}{11}\)
LC
1
LD
16 tháng 5 2022
* Bạn tham khảo nhé *
1212 ++ 1616 ++ 112112 ++ 120120 ++ 130130 ++ 142142 ++ 156156
== 11×211×2 ++ 12×312×3 ++ 13×413×4 ++ 14×514×5 ++ 15×615×6 ++ 16×716×7 ++ 17×817×8
== 1111 −− 1212 ++ 1212 −− 1313 ++ 1313 −− 1414 ++ 1414 −− 1515 ++ 1515 −− 1616 ++ 1616 −− 1717 ++ 1717 −− 1818
== 1111 −− 1818
== 8888 −− 1818
== 78
H
2
29 tháng 3 2018
\(\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-\frac{1}{30}=\frac{1}{1\cdot2}-\frac{1}{2\cdot3}-\frac{1}{3\cdot4}-\frac{1}{4\cdot5}-\frac{1}{5\cdot6}\)
\(=\frac{1}{1}-\frac{1}{2}-\frac{1}{2}-\frac{1}{3}-\frac{1}{3}-\frac{1}{4}-\frac{1}{4}-\frac{1}{5}-\frac{1}{5}-\frac{1}{6}\)
\(=\frac{1}{1}-\frac{1}{6}=\frac{5}{6}\)
NHỚ K MK NHA. CHÚC BẠN HỌC TỐT
29 tháng 3 2018
1/2 - 1/6 - 1/12 - 1/20 - 1/30
=1/1x2 - 1/2x3- 1/3x4 - 1/4x5 - 1/5x6
=1-1/2 + 1/2-1/3 + 1/3-1/4 + 1/4-1/5 +1/5-1/6
=1-1/6
=5/6
SC
1
21 tháng 9 2021
\(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\)
\(=\dfrac{1}{2}-\dfrac{1}{6}\)
\(=\dfrac{1}{3}\)
25 tháng 8 2016
\(\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)
\(=\frac{1}{90}-\left(\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-\frac{1}{30}-\frac{1}{42}-\frac{1}{56}-\frac{1}{72}\right)\)
\(=\frac{1}{90}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)\)
\(=\frac{1}{90}-\left(1-\frac{1}{9}\right)\)
\(=\frac{1}{90}-\frac{8}{9}\)
\(=\frac{-79}{90}\)
25 tháng 8 2016
1/90 - 1/72 - 1/56 - ... - 1/6 - 1/2
= 1/90 - (1/2 + 1/6 + ... + 1/56 + 1/72)
= 1/90 - (1/1×2 + 1/2×3 + ... + 1/7×8 + 1/8×9)
= 1/90 - (1 - 1/2 + 1/2 - 1/3 + ... + 1/7 - 1/8 + 1/8 - 1/9)
= 1/90 - (1 - 1/9)
= 1/90 - 8/9
= 1/90 - 80/90
= -79/90
R
7 tháng 2 2022
\(A=\dfrac{5}{7}.\dfrac{5}{11}+\dfrac{5}{7}.\dfrac{8}{11}-\dfrac{5}{7}.\dfrac{2}{11}\)
\(A=\dfrac{5}{7}.\left(\dfrac{5}{11}+\dfrac{8}{11}-\dfrac{2}{11}\right)\)
\(A=\dfrac{5}{7}.\dfrac{5+8-2}{11}\)
\(A=\dfrac{5}{7}.\dfrac{11}{11}\)
\(A=\dfrac{5}{7}.1=\dfrac{5}{7}\)
\(B=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{35}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{63}\)
\(B=\dfrac{95}{72}\)
\(C=\dfrac{4^6.9^5+6^9.120}{8^4-3^{12}-6^{11}}\)
\(C=\dfrac{\left(2^2\right)^3.\left(3^2\right)^5+\left(2.3\right)^9.2^3.3.5}{\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}\)
\(C=\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(C=\dfrac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.5}\)
\(C=\dfrac{2.6}{5.3}=\dfrac{12}{15}=\dfrac{4}{5}\)
MG
28 tháng 4 2018
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20
=(1+19)+(2+18)+(3+17)+(4+16)+(5+15)+(6+14)+(7+13)+(8+12)+(9+11)+20+10
=20+20+20+20+20+20+20+20+20+20+10
=20×10+10
=200+10
=210
28 tháng 4 2018
= ( 1 + 19 ) + ( 2 + 18 ) + ( 3 + 17 ) + (4 + 16 ) + ( 5 + 15 ) + ( 6 + 14 ) + ( 7 + 13 ) + ( 8 + 12) + ( 9+ 11 ) + 20
= 20 + 20 + 20 +20 + 20 +20 + 20 + 20 + 20 +20
= 20 x 10
= 200
tui đầu tiên đó
Ta có:
12+16+112+120=2−12+3−26+4−312+5−420=22−12+36−26+412−312+520−420=1−12+12−13+13−14+14−15=1−(12−12)−(13−13)−(14−14)−15=1−0−0−0−15=1−15=55−15=45
Chúc em hok tốt nha!☘
Tính bằng cách nhanh nhất
\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}\\ =\dfrac{1\times6}{2\times6}+\dfrac{1\times2}{6\times2}+\dfrac{1}{12}+\dfrac{1}{20}\\ =\dfrac{6}{12}+\dfrac{2}{12}+\dfrac{1}{12}+\dfrac{1}{20}\\ =\dfrac{6+2+1}{12}+\dfrac{1}{20}\\ =\dfrac{9}{12}+\dfrac{1}{20}\\ =\dfrac{3}{4}+\dfrac{1}{20}\\ =\dfrac{3\times5}{4\times5}+\dfrac{1}{20}\\ =\dfrac{15}{20}+\dfrac{1}{20}\\ =\dfrac{15+1}{20}\\ =\dfrac{16}{20}\\ =\dfrac{4}{5}.\)