Tính tổnga) \(\frac{1}{2.4}\) + \(\frac{1}{4.6}\) + \(\frac{1}{6.8}\) +........+ \(\frac{1}{98.100}\) ( Nhân 2 vào 2 vế )b) \(\frac{1}{1.5}\) + \(\frac{1}{5.9}\) + \(\frac{1}{9.13}\) +........+ \(\frac{1}{201.205}\)c) \(\frac{6}{3.5}\) + \(\frac{6}{5.7}\) + \(\frac{6}{7.9}\) +..........+ \(\frac{6}{97.99}\) ( đặt thừa số 3 ra ngoài )d) \(\frac{4}{8.11}\) + \(\frac{4}{11.14}\) + \(\frac{4}{14.17}\) +........+ \(\frac{4}{98.101}\) ( nhân 3 vào 2 vế,...
Đọc tiếp
Tính tổng
a) \(\frac{1}{2.4}\) + \(\frac{1}{4.6}\) + \(\frac{1}{6.8}\) +........+ \(\frac{1}{98.100}\) ( Nhân 2 vào 2 vế )
b) \(\frac{1}{1.5}\) + \(\frac{1}{5.9}\) + \(\frac{1}{9.13}\) +........+ \(\frac{1}{201.205}\)
c) \(\frac{6}{3.5}\) + \(\frac{6}{5.7}\) + \(\frac{6}{7.9}\) +..........+ \(\frac{6}{97.99}\) ( đặt thừa số 3 ra ngoài )
d) \(\frac{4}{8.11}\) + \(\frac{4}{11.14}\) + \(\frac{4}{14.17}\) +........+ \(\frac{4}{98.101}\) ( nhân 3 vào 2 vế, đặt số 4 ra ngoài )
a ) 1/2 .4 + 1/4 . 6 + 1/6 . 8 + .........+ 1/98 . 100
= 1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + ........+ 1/98 - 1/100
= 1/2 - 1/100
= 49/100
b ) 1/1 . 5 + 1/5 . 9 + 1/9 . 13 + ......+ 1/201 . 205
= 1 - 1/5 + 1/5 - 1/9 + 1/9 - 1/13+ ..... + 1/201 - 1/205
= 1 - 1/205
= 204/205
c ) 6/3 . 5 + 6/5 . 7 + 6/7 . 9 + ...... + 6/97 . 99
= 6/3 - 6/5 + 6/5 - 6/7 + 6/7 -6/9 + ........ + 6/97 - 6/99
= 6/3 - 6/99
= 64/33
d ) 4/8 . 11 + 4/11 . 14 + 4/14 . 17 + ......... 4/98 . 101
= 4/8 - 4/11 + 4/11 - 4/14 + 4/14 - 4/17 + .......+ 4/98 - 4/101
= 4/8 - 4/101
= 93/202
a) \(=\frac{1}{2}\times\left(\frac{2}{2\times4}+\frac{2}{4\times6}+....+\frac{2}{98\times100}\right)\)
\(=\frac{1}{2}\times\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{98}-\frac{1}{100}\right)\)
= \(\frac{1}{2}\times\left(\frac{1}{2}-\frac{1}{100}\right)\)
\(=\frac{1}{2}\times\frac{98}{200}=\frac{49}{200}\)