140.28

bạn giải ra đi

3s1=(2.3+3.4+4.5+5.6+...+15.16+16.17).3

3s1=2.3.3+3.4.3+4.5.3+5.6.3+....+15.16.3+16.17.3

3s1=2.3(4-1)+3.4(5-2)+4.5(6-3)+5.6(7-4)+...+15.16(17-14)+16.17(18-15)

3s1=2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+...+15.16.17-14.15.16+16.17.18-15.16.17

3s1=(16.17.18-1.2.3)/3

s1=1630

Ta có: A = 15.16 + 16.17 + 17.18 + 18.19 + ... + 29.30
=> 4A = 4( 15.16 + 16.17 + 17.18 + 18.19 + ... + 29.30)
=> 4A = 15.16.17.4 + 16.17.18.4 + 17.18.19.4 +...... +28.29.30.4
=> 4A = 15.16.17.4 + 16.17.18(5 - 1) + 3.4.5.(6 - 2) +..... +17.18.19.(20 - 16)

A=240+272+306=818

A= 15.16+16.17+17.18

A=818

5/15.16+5/16.17+5/17.18+5/18.19+5/19.20

=5(1/15-1/16+1/16-1/17+..+1/19-1/20) 

=5.(1/15-1/20)

=5.1/60

=1/12

\(\frac{5}{15.16}+\frac{5}{16.17}+\frac{5}{17.18}+\frac{5}{18.19}+\frac{5}{19.20}\)

= \(5.\left(\frac{1}{15.16}+\frac{1}{16.17}+\frac{1}{17.18}+\frac{1}{18.19}+\frac{1}{19.20}\right)\)

= \(5.\left(\frac{1}{15}-\frac{1}{16}+\frac{1}{16}-\frac{1}{17}+\frac{1}{17}-\frac{1}{18}+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)

= \(5.\left(\frac{1}{15}-\frac{1}{20}\right)\)

= \(5.\frac{1}{60}\)

= \(\frac{1}{12}\)

\(\frac{5}{15.16}+\frac{5}{16.17}+\frac{5}{17.18}+\frac{5}{18.19}+\frac{5}{19.20}\)

\(=5\left(\frac{1}{15.16}+\frac{1}{16.17}+...+\frac{1}{19.20}\right)\)

\(=5\left(\frac{1}{15}-\frac{1}{16}+\frac{1}{16}-\frac{1}{17}+...+\frac{1}{19}-\frac{1}{20}\right)\)

\(=5\left(\frac{1}{15}-\frac{1}{20}\right)\)

\(=5.\frac{1}{60}\)

\(=\frac{1}{12}\)

Ta có: 3S = 1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2)  + .....+ 50.51.(52 -49) 

              = 1.2.3 - 0  + 2.3.4 - 1.2.3 + 3.4.5 -2.3.4 + .....+ 50.51.52 - 49.50.51

 3S = 50.51.52

  S = 50.17.52 =44200

Barack mới tự học toán 6 hơn 1 tuần, có cách giải này

= 10² + 10 + 11² + 11 + 12² + 12 + 13² + 13 + 14² + 14 + 15² + 15 +16² +16 +17² +17 + 18² + 18 + 19² +19 

= 10² + 11² + 13² + 14² + 15² + 16² + 17² + 18² +19² + 10 + 11 +12 +13 + 14 + 15 + 16 +17 + 18 + 19

Lớp 6 gì xương thế

Bài này là cơ bản luôn đó:
= 3.(1/1.2 + 1/2.3+...)
= 3.(1/1-1/2+1/2-1/3...)
(tự viết nốt và tính)

A=2(1-3)+4(5-3)+ 6(5-7)+...+50(49-57)

A=-4-8-12-...-100 = -(4+8+12+...+100) (tính tổng cấp số cộng)

\(\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{50.51}\)

\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{50}-\frac{1}{51}\)

\(=\frac{1}{3}-\frac{1}{51}\)

\(=\frac{17}{51}-\frac{1}{51}\)

\(=\frac{16}{51}\)