11+12+13+14+15+16+17+18+19+...+89+88+87+86+85+84+83+82

=( 11 + 89 )+(12+88)+(13+87)+(14+86)+(15+85)+(16+84)+(17+83)+(18+82)+19

=100+100+100+100+100+100+100+100+19

=800+19

=819

1+2+3+4+5+6+7+8+9+11+12+13+14+15+16+17+18+19

=(1+19)+(2+18)+(3+17)+(4+16)+(5+15)+(6+14)+(7+13)+(8+12)+(9+11)

=20+20+20+20+20+20+20+20+20

=20x9

=180

\(1+2+3+4+5+6+7+8+9+11+12+13+14+15+16+17+18+19\)

\(=\left(1+19\right)+\left(2+18\right)+\left(3+17\right)+\left(4+16\right)+\left(5+15\right)+\left(6+14\right)+\left(7+13\right)+\left(8+12\right)+\left(9+11\right)\)\(=20+20+20+20+20+20+20+20+20\)

\(=20\times9\)

\(=180\)

11 x 12 + 12 x 13 + 13 x 14 + 14 x 15 + 15 x 16 + 16 x 17 + 17 x 18 + 18 x 19 + 19 x 20 + 20 x 21

= 12 x ( 11 + 13 ) + 14 x ( 13 + 15 ) + 16 x ( 15 + 17 ) + 18 x ( 17 + 19 ) + 20 x 21

= 12 x 24 + 14 x 28 + 16 x 32 + 18 x 36 + 420

= 288 + 392 + 512 + 648 + 420

= ( 288 + 392 ) + ( 512 + 648 ) + 420 

= 680 + 1160 + 420

= 1840 + 420

= 2260

tk nha

= 

Ta có:

    11 x 12 + 12 x 13 + 13 x 14 + 14 x 15 + 15 x 16 + 16 x 17 + 17 x 18 + 18 x 19 + 19 x 20 + 20 x 21

= 12 x ( 11 + 13 ) + 14 x ( 13 + 15 ) + 16 x ( 15 + 17 ) + 18 x ( 17 + 19 ) + 20 x 21

= 12 x 24 + 14 x 28 + 16 x 32 + 18 x 36 + 420

= 288 + 392 + 512 + 648 + 420

= ( 288 + 392 ) + ( 512 + 648 ) + 420 

= 680 + 1160 + 420

= 1840 + 420

= 2260

#Mạt Mạt#

= (11+19) + (12+18) + (13+17) + (14+16) + (10+15)

= 30 + 30 + 30 + 30 + 25 = 145

A = 10 + (11 + 19) + (12 + 18) + (13 + 17) + (14 + 16) + 15

= 10 + 30 + 30 + 30 + 30 + 15 = 145

10 + 11 + 12 + 13 + 14 + 15 + 15 + 16 + 17 + 18 + 19 + 20

= ( 10 + 20 ) + ( 11 + 19 ) + ( 12 + 18 ) + ( 13 + 17 ) + ( 14 + 16 ) + ( 15 + 15 )

= 30 + 30 + 30 + 30 + 30 +30 

= 30 x 6

= 180 .

10+11+12+13+14+15+16+17+18+19+20=165

đầu bài: 1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20

= (1+19)+(2+18)+(3+17)+(4+16)+(5+15)+(6+14)+(7+13)+(8+12)+(9+11)+20

=    20   +   20   +   20   +    20  +   20  +    20  +   20   +   20   +   20   +20

=   20.10

=   200

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20=\(\frac{\left(1+20\right)20}{2}\)=210

Gọi \(S=\frac{15}{15\cdot16}+\frac{15}{16\cdot17}+..+\frac{15}{19\cdot20}\)

\(\Leftrightarrow S=1-\frac{15}{16}+\frac{15}{16}-\frac{15}{17}+...+\frac{15}{19}-\frac{15}{20}\)

\(\Leftrightarrow S=1-\frac{15}{20}=\frac{1}{4}<\frac{1}{3}\)

Vậy S< \(\frac{1}{3}\)

--------------------Good luck------------------------

15 nha

Ta có: 1+2+3+…+20=20.(20+1):2=20.21:2=420:2=210

khoảng cách: 2-1=1

số số hạng là: (20-1):1+1=20(số)

tổng là: (20+1)x20:2=210