Ai giup minh cau nay voi
B=\(\frac{1}{1\times2}\)+\(\frac{1}{2\times3}\)+\(\frac{1}{3\times4}\)+...+\(\frac{1}{2017\times2018}\)
Tính nhanh:
a)\(\frac{131313}{151515}+ \frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)
b)\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{2017\times2018}\)
c)\(\frac{1}{3\times5}+\frac{1}{4\times7}+\frac{1}{7\times9}+...\frac{1}{2015\times2017}+\frac{1}{2017\times2018}\)
\(a,\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)
\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
\(=13\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{7.9}\right)\)
\(=13\left(\frac{1}{3}-\frac{1}{9}\right)\)
\(=13.\frac{2}{9}=\frac{26}{9}\)
\(b,\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2017}-\frac{1}{2018}\)
\(=1-\frac{1}{2018}=\frac{2017}{2018}\)
P/s :Dấu chấm là dấu nhân nha
\(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)
\(=\frac{13.10101}{15.10101}+\frac{13.10101}{35.10101}+\frac{13.10101}{63.10101}+\frac{13.10101}{99.10101}\)
\(=13.\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\right)\)
\(=\frac{13}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)
\(=\frac{13}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
\(=\frac{13}{2}.\left(\frac{1}{3}-\frac{1}{11}\right)\)
\(=\frac{13}{2}.\left(\frac{11}{33}-\frac{3}{33}\right)\)
\(=\frac{13}{2}.\frac{8}{33}\)
\(=\frac{52}{33}\)
\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2017.2018}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2017}-\frac{1}{2018}\)
\(=1-\frac{1}{2018}\)
\(=\frac{2017}{2018}\)
Sửa đề chút:
\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{2015.2017}+\frac{1}{2017.2018}\)
\(=\frac{1}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{2015.2017}\right)+\frac{1}{2017}-\frac{1}{2018}\)
\(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2015}-\frac{1}{2017}\right)+\frac{1}{2017}-\frac{1}{2018}\)
\(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{2017}\right)+\frac{1}{2017}-\frac{1}{2018}\)
B tự làm nốt nhé
Cho B= \(\frac{1\times2}{1\times2\times3}+\frac{1\times2}{1\times2\times4}+\frac{1\times2}{1\times2\times3\times4}+\frac{1\times2}{1\times2\times3\times4\times5}+....+\frac{1\times2}{n,giao}\left(n\in N,n\ge3\right)\)
chứng tỏ B nhỏ hơn 3
Tính\(\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+...\frac{1}{2014\times2015\times2016}\)
\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{2014.2015.2016}\)
\(=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{2014.2015.2016}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{2014.2015}-\frac{1}{2015.2016}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2015.2016}\right)\)
\(\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+...+\frac{1}{2014\times2015\times2016}=?\)
= 1/2 .( 1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + 1/3.4 - 1/4.5 + .......+ 1/2014.2015 - 1/2015.2016)
= 1/2 ( 1/2 - 1/2015.2016)
Tính tiếp p nhé.
Tim X .
Cau 1 : x : ( \(\frac{1}{1\times3}\) + \(\frac{1}{3\times5}\) + ...... + \(\frac{1}{101\times103}\)) = 1
Cau 2 : (\(\frac{1}{1\times2}\) + \(\frac{1}{2\times3}\) + \(\frac{1}{3\times4}\) + ......... + \(\frac{1}{11\times12}\) ) \(\times\) X = 2
cac ban giup minh nha. Minh dang can gap
Câu 1 :
\(x:\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{101.103}\right)=1\)
\(=>x:\left[\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{101}-\frac{1}{103}\right)\right]\) \(=1\)
\(=>x:\left[\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{103}\right)\right]=1\)
\(=>\) \(x:\frac{51}{103}=1\)
\(=>x=1.\frac{51}{103}=\frac{51}{103}\)
Câu 2 :
\(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{12.13}\right).x=2\)
\(=>\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\right).x=2\)
\(=>\left(\frac{1}{1}-\frac{1}{12}\right).x=2\)
\(=>\frac{11}{12}.x=2\)
\(=>x=2:\frac{11}{12}\)
\(=>x=\frac{24}{11}\)
cau b bang 24/11
Cau a bang 51/103
=\(\left(1+\frac{1}{1\times3}\right)\left(1+\frac{1}{2\times4}\right)\left(1+\frac{1}{3\times5}\right)...\left(1+\frac{1}{2016\times2018}\right)\)
Ai giúp với
= 1.3+1/1.3 . 2.4+1/2.4 . ....... . 2016.2018+1/2016.2018
= 2^2/1.3 . 3^2/2.4 . ....... . 2017^2/2016.2018
= 2.3. ...... . 2017/1.2. ..... . 2016 . 2.3. ..... . 2017/3.4. ...... . 2018
= 2017 . 2/2018
= 2017/1009
Tk mk nha
Tính luôn :
= 4/3 . 9/8 . 16/15 .. . 4068289/2016 . 2018
= 4/3 . 9/8 . 16/15 . .. 2017 x 2017 / 2016. 2018
= 4 . 9 . 16 ... 2017 . 2017 / 3 . 8 . 15 . ...2016 . 2018
= 2 . 2 . 3 . 3 . 4 . 4 ... 2017 . 2017 / 3 . 2 . 4 . 3 . 5 ...2016 . 2018
= ( 2 . 3 . 4 ... 2017 ) . ( 2 . 3 . 4 ... 2017 ) / ( 3 . 4 . 5 ... 2016 ) . ( 2 . 3 . 4 . 5 ...2018 )
= 2 . 2017 / 2018
= 2017 / 1009
Thực hiện phép tính:
a)\(1\times2\times3\times......\times9-1\times2\times3\times......\times8-1\times2\times3\times.....\times8\times8\)
b)\(B=\frac{\left(3\times4\times2^{16}\right)^2}{11\times2^{13}\times4^{11}-16^9}\)
c)\(C=70\times\left(\frac{131313}{565656}+\frac{131313}{727272}+\frac{131313}{909090}\right)\)
d)\(B=\frac{1}{4\times9}+\frac{1}{9\times14}+\frac{1}{14\times19}+...+\frac{1}{64\times69}\)
GIÚP MIK VỚI AI NHANH MIK CHO 3 TICK LUÔN CHO NHA!!!!!!!!!!NHỚ TRÌNH BÀY RÕ RÀNG NHA!!!!!!HELP ME
a)1.2.3.4...9-1.2.3.4...8-1.2.3.4...8.8
=1.2.3.4...8(9-1-8)
=1.2.3.4...8.0
=0
b)(3.4.216)2/11.123.411-169=(3.22.216)2/11.213.222-236=32.24.232/11.235-236=32.226/235.(11-2)
=32.236/235.9=32.236/235.32=2
c)70.(131313/565656+131313/727272+131313/909090
=70.(13/56+13/72+13/90)
=70.39/70=39
d)1/4.9+1/9.14+1/14.19+...+1/64.69
=4/4.9.4+4/9.4.14+4/14.19.4+...+4/64.69.4.
=1/4.(4/4.9+4/9.14+4/14.19+...+4/64.69)
=1/4.(1/4-1/9+1/9-1/14+1/14-1/19+...+1/64-1/69)
=1/4.(1/4-1/69)
=1/4.65/276=65/1104
~~~~~~~~Chúc bạn học giỏi nhé !~~~~~~~~
d)\(\frac{1}{3}\times\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{64}-\frac{1}{69}\right)\)
\(\frac{1}{3}\times\left(\frac{1}{4}-\frac{1}{69}\right)\)
\(\frac{1}{3}\times\frac{65}{276}\)
\(\frac{1\times2}{2\times3}+\frac{2\times3}{3\times4}+\frac{3\times4}{4\times5}+...+\frac{98\times99}{99\times100}\)
\(=\frac{1.2}{99.100}\)
\(=\frac{2}{9900}=\frac{1}{4950}\)
A =\(\frac{1}{1\times2}+\frac{1}{3\times4}+\frac{1}{5\times6}+...+\frac{1}{2017\times2018}\)
B= \(\frac{1}{2010.2018}+\frac{1}{2011.2017}+\frac{1}{2012.2016}+...\frac{1}{2018.2010}\)
CMR \(\frac{a}{b}\) là số nguyên