a) \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{2017\cdot2018}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2017}-\frac{1}{2018}\)

\(=1-\frac{1}{2018}\)

\(=\frac{2017}{2018}\)

b) \(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{97\cdot99}\)( sửa 91.99 thành 97.99 mới đúng nha )

\(=\frac{1}{2}\left(\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+...+\frac{2}{97}-\frac{2}{99}\right)\)

\(=\frac{1}{2}\left(\frac{2}{3}-\frac{2}{99}\right)\)

\(=\frac{1}{2}.\frac{64}{99}\)

\(=\frac{32}{99}\)

a) 1/1.2 + 1/2.3 + 1/3.4 +...+1/2017.2018

= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ....+1/2017 - 1/2018

= 1 - 1/2018 

= 2017/2018

a,79.101=79.(100+1)

= 79.100 + 79

=7900 + 79 = 7979

b,(1999+2016)-1999 = 1999 - 1999 + 2016 = 0 + 2016 = 2016

c,81+250+19 =(81 + 19) + 250 = 100 + 250 = 350

d,165+79+135 =(165+135)+79=300+79=379

e,35.45+35.55=35.(45+55)

= 35.100

=3500

f,5.125.2.8=(5.2).(125.8)

= 10 . 1000

= 10 000

a) 79. 101

= 79 . (100 + 1)

= 79. 100 + 79

= 7 900 + 79

= 7 979

b) (1 999 + 2 016) - 1 999

= ( 1 999 - 1 999) + 2 016

= 0 + 2 016

= 2 016

c) 81 + 250 + 19

= (81 + 19) + 250

= 100 + 250

= 350

d) 165 + 79 + 135

= (165 + 135) + 79

= 300 + 79

= 379

e) 35 . 45 + 35 . 55

= 35 . (45 + 55)

= 35. 100

= 3 500

f) 5. 125 . 2. 8

= (5 . 2) . (125 . 8)

= 10 . 1 000

= 10 000

Bài 1 :

a, 2013 - 79 -1013 - 21

= (2013 -1013 ) + (-79 -21 )

=1000 - 100

=900

b, 135 - 591 -409 +437

= ( 135 + 437 ) +(-591 -409 )

= 572 -1000

= -428

c, -46 - 135 +35 +146

= 100 -100

= 0

a) 2013-79-1013-21

=(2013-1013)-(-79-21)

=1000-100

=900

b) 135-591-409+437

=(135+437)-(-591-409)

= 572-1000

= -428

c) -46-135+35+146

= (-46+146)+(-135+35)

=100+(-100)

=0

Ở 2 phép tính đầu thì là chuyển a và số sang, ko có gì đặc biệt.

Ở phép tính 2 với 3 là sai vì \(\left(2a+1\right)^2-4^2=4a^2+4a+1-16=4a^2+4a-15\)

Nếu đúng thì ở phép tính 3 phải là: \(2\left[\left(2a+1\right)^2-4^2\right]\)

Bạn làm sai rồi!

Ta có: 49a² + 49a + 49 = 57a² + 57a + 19

\(\Leftrightarrow\) 49a² + 49a + 49 - 57a^{2 -} 57a - 19 = 0

\(\Leftrightarrow\) -8a² - 8a + 30 = 0

\(\Leftrightarrow\) -2(4a² + 4a - 15) = 0

\(\Leftrightarrow\) -2\(\left[\left(2a\right)^2+2.2a.1+1^2-16\right]\)= 0

\(\Leftrightarrow\) \(-2\left[\left(2a+1\right)^2-4^2\right]=0\)

\(\Leftrightarrow\) \(\left(2a+1\right)^2-4^2=0\)

\(\Leftrightarrow\) \(\left(2a+1+4\right)\left(2a+1-4\right)=0\)

\(\Leftrightarrow\) \(\left(2a+5\right)\left(2a-3\right)=0\)

\(\Leftrightarrow\)\(\left[{}\begin{matrix}2a+5=0\\2a-3=0\end{matrix}\right.\)

\(\Leftrightarrow\) \(\left[{}\begin{matrix}2a=-5\\2a=3\end{matrix}\right.\)

\(\Leftrightarrow\) \(\left[{}\begin{matrix}a=-\dfrac{5}{2}\\a=\dfrac{3}{2}\end{matrix}\right.\)

a) \(S_1=1+2+3+4+......+999\)

\(\Rightarrow S_1=\dfrac{\left(999+1\right).\left[\left(999-1\right):1+1\right]}{2}\)

\(\Rightarrow S_1=\dfrac{1000.\left(998+1\right)}{2}\)

\(\Rightarrow S_1=\dfrac{1000.999}{2}\)

\(\Rightarrow S_1=\dfrac{999000}{2}\)

\(\Rightarrow S_1=499500\)

b) \(S_2=10+12+14+......+2010\)

\(\Rightarrow S_2=\dfrac{\left(2010+10\right).\left[\left(2010-10\right):2+1\right]}{2}\)

\(\Rightarrow S_2=\dfrac{2020.\left(2000:2+1\right)}{2}\)

\(\Rightarrow S_2=\dfrac{2020.\left(1000+1\right)}{2}\)

\(\Rightarrow S_2=\dfrac{2020.1001}{2}\)

\(\Rightarrow S_2=\dfrac{2022020}{2}\)

\(\Rightarrow S_2=1011010\)

c) \(S_3=21+23+25+.......1001\)

\(\Rightarrow S_3=\dfrac{\left(1001+21\right).\left[\left(1001-21\right):2+1\right]}{2}\)

\(\Rightarrow S_3=\dfrac{1022.\left(980:2+1\right)}{2}\)

\(\Rightarrow S_3=\dfrac{1022.\left(490+1\right)}{2}\)

\(\Rightarrow S_3=\dfrac{1022.491}{2}\)

\(\Rightarrow S_3=\dfrac{501802}{2}\)

\(\Rightarrow S_3=250901\)

d) \(S_5=1+4+7+......+79\)

\(\Rightarrow S_5=\dfrac{\left(79+1\right).\left[\left(79-1\right):3+1\right]}{2}\)

\(\Rightarrow S_5=\dfrac{80.\left(78:3+1\right)}{2}\)

\(\Rightarrow S_5=\dfrac{80.\left(26+1\right)}{2}\)

\(\Rightarrow S_5=\dfrac{80.27}{2}\)

\(\Rightarrow S_5=\dfrac{2160}{2}\)

\(\Rightarrow S_5=1080\)

e) \(S_7=15+25+35+45+......+115\)

\(\Rightarrow S_7=\dfrac{\left(115+15\right).\left[\left(115-15\right):10+1\right]}{2}\)

\(\Rightarrow S_7=\dfrac{130.\left(100:10+1\right)}{2}\)

\(\Rightarrow S_7=\dfrac{130.\left(10+1\right)}{2}\)

\(\Rightarrow S_7=\dfrac{130.11}{2}\)

\(\Rightarrow S_7=\dfrac{1430}{2}\)

\(\Rightarrow S_7=715\)

91x99=9009 nha bạn!!

tík mình nha!!

91x99=9009

tíc nha 

bạn

91 . 99 = 9009

mình nhanh nhất kick mình nha

D

Chọn D

1=1x1

4=2x2

9=3x3...

36=6x6

49=7x7

64=8x8