\(\frac{3}{2^2}\)+\(\frac{5}{6^2}\)+\(\frac{7}{12^2}\)+ ....+\(\frac{19}{90^2}\)

= \(\frac{3}{4}\)+\(\frac{5}{36}\)+\(\frac{7}{144}\)+....+\(\frac{19}{8100}\)

= (\(\frac{3}{4}\)+\(\frac{5}{36}\)+\(\frac{7}{144}\)) + .... \(\frac{19}{8100}\)

= (\(\frac{108}{144}\)+\(\frac{20}{144}\)+\(\frac{7}{144}\)) +....+\(\frac{19}{8100}\)

= \(\frac{108+20+7}{144}\)+....+\(\frac{19}{8100}\)

=\(\frac{135}{144}\)+....+\(\frac{19}{8100}\)

=\(\frac{7593,75}{8100}\)+....+\(\frac{19}{8100}\)

=\(\frac{7593,75}{8100}\)+\(\frac{19}{8100}\)

=\(\frac{7593,75+19}{8100}\)

=\(\frac{7612,75}{8100}\)

mik không chắc đúng không?

=3/4+5/36+......+19/8100

=3/1.4+5/4.9+.............+19/81.100

=1/1-1/4+1/4-1/9+...............+1/81-1/90

=1/1-1/90=1-1/90=89/90

\(\frac{3}{2^2}+\frac{5}{6^2}+\frac{7}{12^2}+...+\frac{19}{90^2}\)

= \(\frac{3}{2^2}\)+ \(\frac{5}{2^2.3^2}\)+\(\frac{7}{2^2.6^2}\)+ .... + \(\frac{19}{2^2.45^2}\)

=\(\frac{3}{2^2}\)+\(\frac{5}{2^2}\)-\(\frac{5}{3^2}\)+ \(\frac{7}{2^2}\)-\(\frac{7}{6^2}\)+ .... +\(\frac{19}{2^2}\)-\(\frac{9}{45^2}\)

=\(\frac{3+5+7+9+11+13+15+17+19}{2^2}\)-(tự làm)

= \(\frac{99}{4}\)-(tự làm)

Mấy câu như này tách ra kiểu gì?

\(\frac{5}{12}+\frac{5}{20}+\frac{5}{30}+...+\frac{5}{9900}=\frac{5}{3.4}+\frac{5}{4.5}+\frac{5}{5.6}+...+\frac{5}{99.100}\)

\(5\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(5\left(\frac{1}{3}-\frac{1}{100}\right)=\frac{97}{60}\)

\(\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+...+\frac{71}{72}+\frac{89}{90}=1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+...+1-\frac{1}{90}\)

\(=8-\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)

\(=8-\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)

\(=8-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(=8-\left(\frac{1}{2}-\frac{1}{10}\right)=8-\frac{2}{5}=\frac{38}{5}\)

3/1².2² + 5/2².3² + 7/3².4² + ... + 19/9².10²

= 3/1.4 + 5/4.9 + 7/9.16 + ... + 19/81.100

= 1 - 1/4 + 1/4 - 1/9 + 1/9 - 1/16 + ... + 1/81 - 1/100

= 1 - 1/100

= 99/100

\(A=\frac{3}{1.4}+\frac{5}{4.9}+\frac{7}{9.16}+..+\frac{17}{64.81}+\frac{19}{81.100}\)

\(A=\frac{4-1}{1.4}+\frac{9-4}{4.9}+\frac{16-9}{9.16}+...+\frac{81-64}{64.81}+\frac{100-81}{81.100}\)

\(A=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+...+\frac{1}{61}-\frac{1}{81}+\frac{1}{81}-\frac{1}{100}\)

\(A=1-\frac{1}{100}=\frac{99}{100}\)

\(a,=\left(\frac{15}{12}-\frac{3}{12}\right)+\left(\frac{5}{13}-\frac{18}{13}\right)\)

\(=1+-1\)

\(=0\)

I'm sorry, I can't help you

a) câu a sai đề em nhé, tử số phải là 6/ 13

tử số em đặt 3 ra ngoài, mẫu số em đặt 11 ra ngoài bên trong ngoặc là hai biểu thức giống nhau, đáp số 3/11

b) 17^18 = (17^3)^6 =4913^6

63^12 =(63^2)^6 =3969^6. giờ thì dễ rồi

c) Vì ( x - √3 )^ 2016 >= 0;  ( y ^2 -3 ) ^ 2018> =0 nên ( x - √3 )^ 2016 + ( y ^2 -3 ) ^ 2018 = 0 khi ( x - √3 )^ 2016 =0 và

 ( y ^2 -3 ) ^ 2018 = 0,  suy ra x = căn 3; y^2 =3 => x =căn 3; y = căn 3 hoặc y = - căn 3

tự làm

a,\(\frac{4}{9}.\frac{2}{6}=\frac{4}{27}\)

b,\(1\frac{1}{3}.\left(0,5\right)+\left(\frac{8}{15}-\frac{19}{30}\right):\frac{6}{15}\)

=\(\frac{4}{3}.\frac{1}{2}+\left(\frac{16}{30}-\frac{19}{30}\right).\frac{15}{6}\)

=\(\frac{2}{3}+\frac{-1}{10}.\frac{15}{6}\)

=\(\frac{2}{3}+\frac{-1}{4}\)

=\(\frac{8}{12}+\frac{-3}{12}=\frac{5}{12}\)

bài2

a,\(\left(\frac{2}{7}.x+\frac{3}{7}\right):2\frac{1}{5}-\frac{3}{7}=1\)

=>\(\left(\frac{2}{7}.x+\frac{3}{7}\right):\frac{11}{5}=1+\frac{3}{7}=\frac{10}{7}\)

=>\(\frac{2}{7}.x+\frac{3}{7}=\frac{10}{7}.\frac{11}{5}\)

=>\(\frac{2}{7}.x+\frac{3}{7}=\frac{22}{7}\)

=>\(\frac{2}{7}.x=\frac{22}{7}-\frac{3}{7}=\frac{19}{7}\)

=>\(x=\frac{19}{7}:\frac{2}{7}=\frac{19}{7}.\frac{7}{2}=\frac{19}{2}\)

vậy x\(=\frac{19}{2}\)