tham khảo:

99/100

1/1+(-2)+3+(-4)+.....+19+(-20)

=1-2+3-4+.....+19-20

=(1+3+.....+19)-(2+4+.....+20)

={(19+1).[(19-1):2+1]:2}-{(20+2).[(20-2):2+1]:2}

={20.10:2}-{22.10:2}

=10:2.(20-22)

=5.(-2)

=-10

các ý sau bạn làm theo mẫu nhé                                'cô_bé_DuDu'

5454 nha

\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{49\cdot50}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-.....+\frac{1}{49}-\frac{1}{50}\)

\(=\frac{1}{2}-\frac{1}{50}\)

\(=\frac{24}{50}=\frac{12}{25}\)

\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{49\cdot50}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{50}\)

\(=\frac{1}{2}-\frac{1}{50}\)

\(=\frac{12}{25}\)

\(E=-\frac13\left(1+2+3\right)-\frac14\left(1+2+3+4\right)-\cdots-\frac{1}{50}\left(1+2+3+\cdots+50\right)\)

\(=-\frac13\cdot\frac{3\cdot4}{2}-\frac14\cdot\frac{4\cdot5}{2}-\cdots-\frac{1}{50}\cdot\frac{50\cdot51}{2}\)

\(=-\frac42-\frac52-\cdots-\frac{51}{2}=-\frac12\left(4+5+\cdots+51\right)\)

\(=-\frac12\cdot\frac{\left(51-4+1\right)\left(51+4\right)}{2}=-\frac12\cdot\frac{48\cdot55}{2}=-\frac12\cdot24\cdot55=-12\cdot55=-660\)

a, thì dễ rồi bạn tự làm nhé 

mk làm câu b thôi 

b,\(\frac{1}{1x2}\)+ \(\frac{1}{2x3}\)+......+\(\frac{1}{99x100}\)

= 1 - \(\frac{1}{2}\)+ \(\frac{1}{2}\)-\(\frac{1}{3}\)+....+\(\frac{1}{99}\)- \(\frac{1}{100}\)

= 1 - \(\frac{1}{100}\)

= \(\frac{99}{100}\)

Giup minh cau a voi ko biet lam