tính nhanh nha
D=\(\frac{3}{2x4}+\frac{3}{4x6}+...+\frac{3}{98x100}\)
A=\(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}\)
B=\(6\frac{2}{3}+7\frac{5}{8}+3\frac{1}{3}+4\frac{5}{8}\)
C=[\(4\frac{2}{5}+2\frac{3}{7}\)] - [\(2\frac{2}{5}-1\frac{4}{7}\)]
E=\(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)
làm ơn giúp mik nha
mik đang cần gấp
mik sẽ tick(chắc chắn lun) cho người nhanh nhất
1/3xD=1/(2x4)+1/(4x6)+...+1/(98x100)
2/3xD=2/(2x4)+2/(4x6)+...+1/(98x100)
2/3xD= 1/2-1/4+1/4-1/6+...+1/98-1/100
2/3xD=1/2-1/100
2/3xD=49/100
D=147/200
A=1/2+1/3+1/6+1/12
A=(1/2+1/3+1/6)+1/12
A=1+1/12
A=13/12
B=20/3+61/8+10/3+37/8
B=30/3+98/8
B=10+49/4
B=89/4
\(D=\frac{3}{2\cdot4}+\frac{3}{4\cdot6}+...+\frac{3}{98\cdot100}=\frac{3}{2}\left[\frac{1}{2\cdot4}+\frac{1}{4\cdot6}+...+\frac{1}{98\cdot100}\right]\)
\(D=\frac{3}{2}\left[\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\right]=\frac{3}{2}\left[\frac{1}{2}-\frac{1}{100}\right]\)
\(D=\frac{3}{2}\cdot\frac{49}{100}=\frac{147}{200}\)
\(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}=\frac{1}{3}+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}=\frac{1}{3}+\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}\)
\(A=\frac{1}{3}+\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}=\frac{1}{3}+\frac{1}{1}-\frac{1}{4}=\frac{1}{3}+\frac{3}{4}=\frac{13}{12}\)
\(B=6\frac{2}{3}+7\frac{5}{8}+3\frac{1}{3}+4\frac{5}{8}=\left[6+\frac{2}{3}+\frac{1}{3}+3\right]+\left[7+\frac{5}{8}+\frac{5}{8}+4\right]\)
\(B=\left[6+1+3\right]+\left[7+4+\frac{5}{4}\right]=10+11+\frac{5}{4}=21+\frac{5}{4}=\frac{89}{4}\)
\(C=\left[4\frac{2}{5}+2\frac{3}{7}\right]-\left[2\frac{2}{5}-1\frac{4}{7}\right]=4\frac{2}{5}+2\frac{3}{7}-2\frac{2}{5}+1\frac{4}{7}\)
\(C=\left[4\frac{2}{5}-2\frac{2}{5}\right]+\left[2\frac{3}{7}+1\frac{4}{7}\right]=2+4=6\)
\(E=\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)
\(E=\frac{13}{3\cdot5}+\frac{13}{5\cdot7}+\frac{13}{7\cdot9}+\frac{13}{9\cdot11}=\frac{13}{2}\left[\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+\frac{1}{9\cdot11}\right]\)
\(E=\frac{13}{2}\left[\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right]=\frac{13}{2}\left[\frac{1}{3}-\frac{1}{11}\right]\)
\(E=\frac{13}{2}\cdot\frac{8}{33}=\frac{52}{33}\)
ai thấy đúng nhớ nhé
