1+2+3+4+5+...+15+16+17+18+19+20

= ( 1 + 19 ) + ( 2 + 18 ) + ( 3 + 17 ) + ( 4 + 16 ) + ( 5 + 15 ) + ... + ( 9 + 11 ) +  ( 10 + 20 )

= 20 + 20 + 20 + 20 + ... + 20 + 30

= 180 + 30 = 210

Tính số phần tử:   \(\text{1+2+3+4+...+18+19+20}\) 
                              \(=\left(20-1\right):1+1\) \(=20\)

Tổng : \(\dfrac{\left(20+1\right)\times20}{2}=210\)

=10 nha

20 - 19 + 18 - 17 + 16 - 15 +....+ 4-3 + 2 - 1

= ( 20 - 19 ) + ( 18 - 17 ) + ( 16 - 15 ) + .... +  ( 4 - 3 ) + ( 2 - 1 )

= 1 + 1 + 1 + .... + 1 + 1

=> có 10 số 1 

=> Tổng dãy số đó là : 1 . 1 = 10

nguyễn tiến mạnh

20 - 19 + 18 - 17 + 16 - 15 +....+ 4 - 3 + 2 - 1

= ( 20 - 19 ) + ( 18 - 17 ) + ( 16 - 15 ) + .... + ( 4 - 3 ) + ( 2 - 1 )

= 1 + 1 + 1 + .... + 1 + 1

=> có 10 số 1

=> Tổng dãy số đó là : 1 x 10 = 10 

20-19+18-17+16-15+...+4-3+2-1=(20-19)+(18-17)+(16-15)+...+(4-3)+(2-1) (có 10 nhóm)

=1+1+1+...+1+1( có 10 số 1) =10.

(21-20)-(19-18)+(17-16)-(15-14)+...+(5-4)-(3-2)+1=1-1+1-1+...+1-1+1=(1-1)+(1-1)+...+(1-1)+1( có 10 cặp nhóm)

=0+0+...+0+0+1=1.

Giải:

      \(21-20-19+18+17-16-15+14+...+5-4-3+2+1\)

\(=\left(21-20-19+18\right)+\left(17-16-15+14\right)+...+\left(5-4-3+2\right)+1\)

\(=0+0+...+0+1=1\)

10 do ban a cho minh nha

20 - 19 + 18 - 17 + .... + 4 - 3 + 2 -1  =  (20 - 19) + (18 - 17) + (16 - 15) + ... + (4 - 3) + (2 - 1) {Có 10 cặp số}

= 1 + 1 + 1 + ...+ 1 + 1 {Có 10 số 1}

= 1 x 10

= 10

= 10 nha bạn

M = \(15.\left(\frac{1}{15.16}+\frac{1}{16.17}+...+\frac{1}{19.20}\right)\)
= \(15.\left(\frac{1}{15}-\frac{1}{16}+\frac{1}{16}-\frac{1}{17}+...+\frac{1}{19}-\frac{1}{20}\right)\)
= \(15.\left(\frac{1}{15}-\frac{1}{20}\right)\)
= \(15.\frac{1}{60}\)= \(\frac{1}{4}\)\(< \frac{1}{3}\)
(=) \(M< \frac{1}{3}\)\(\left(đpcm\right)\)

Ta có: \(M=\frac{15}{15.16}+\frac{15}{16.17}+\frac{15}{17.18}+\frac{15}{18.19}+\frac{15}{19.20}\)

\(\Rightarrow M=15.\left(\frac{1}{15.16}+\frac{1}{16.17}+\frac{1}{17.18}+\frac{1}{18.19}+\frac{1}{19.20}\right)\)

\(\Rightarrow M=15.\left(\frac{1}{15}-\frac{1}{16}+\frac{1}{16}-\frac{1}{17}+\frac{1}{17}-\frac{1}{18}+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)

\(\Rightarrow M=15.\left(\frac{1}{15}-\frac{1}{20}\right)\)

\(\Rightarrow M=15.\frac{1}{60}=\frac{1}{4}\)

Ta thấy: \(\frac{1}{4}< \frac{1}{3}\Rightarrow M< \frac{1}{3}\)

Vậy \(M< \frac{1}{3}\)

Chúc bạn học tốt!

\(\Rightarrow M=15.\left(\frac{1}{15.16}+\frac{1}{16.17}+...+\frac{1}{19.20}\right)\)

\(M=15.\left(\frac{1}{15}-\frac{1}{16}+\frac{1}{16}-\frac{1}{17}+...+\frac{1}{19}-\frac{1}{20}\right)\)

\(M=15.\left(\frac{1}{15}+\left(-\frac{1}{16}+\frac{1}{16}\right)+\left(-\frac{1}{17}+\frac{1}{17}\right)+...+\left(\frac{-1}{19}+\frac{1}{19}\right)-\frac{1}{20}\right)\)

\(M=15.\left(\frac{1}{15}+0+0+0+...+0-\frac{1}{20}\right)\)

\(M=15.\left(\frac{1}{15}-\frac{1}{20}\right)=\frac{15}{60}\)

Mà \(\frac{1}{3}=\frac{20}{60}\)

\(\Rightarrow M< \frac{1}{3}\)

Vậy : \(M< \frac{1}{3}\)

14) \(\sqrt{7-4\sqrt{3}}=2-\sqrt{3}\)

15) \(\sqrt{8+2\sqrt{15}}=\sqrt{5}+\sqrt{3}\)

16) \(\sqrt{10-2\sqrt{21}}=\sqrt{7}-\sqrt{3}\)

17) \(\sqrt{11+2\sqrt{18}}=3+\sqrt{2}\)

18) \(\sqrt{7+2\sqrt{10}}=\sqrt{5}+\sqrt{2}\)

19) \(\sqrt{7+4\sqrt{3}}=2+\sqrt{3}\)

20) \(\sqrt{12-2\sqrt{35}}=\sqrt{7}-\sqrt{5}\)

\(\sqrt{7-4\sqrt{3}}=\sqrt{2^2-2.2.\sqrt{3}+\left(\sqrt{3}\right)^2}=\sqrt{\left(2-\sqrt{3}\right)^2}=\left|2-\sqrt{3}\right|=2-\sqrt{3}\)

√7−4√3=√22−2.2.√3+(√3)2=√(2−√3)2=∣∣2−√3∣∣=2−√3

1+2+3+4+5+6+7+8+9+10=55

11+12+13+14+15+16+17+18+19+20=155

1+2+3+4+5+6+7+8+9+10+11+12+13+14 +15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30-50-53=362

1+2+3+4+5+6+7+8+9+10=55

11+12+13+14+15+16+17+18+19+20=155

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30-50-53=362