S = 1.2 + 2.3 + 3.4 + ... + 15.16

3S = 1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2) + ... +15.16.(17-14)

3S = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 15.16.17 - 14.15.16

3S = 15.16.17

S = 5.16.17

S = 1360

Bạn nào làm nhanh nhất cho mình cho 2 k !!!

3S=1.2.3+2.3.3+3.4.3+...+15.16.3

3S=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+15.16.(17-14)

3S=0.1.2 - 1.2.3+1.2.3-2.3.4+2.3.4-3.4.5+...+14.15.16-15.16.17

3S=15.16.17

3S=4080

S=4080:3=1360

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{14.15}+\frac{1}{15.16}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{16}\)

\(=1-\frac{1}{16}\)

\(=\frac{15}{16}\)

Chúc bạn học giỏi nha!!!

K cho mik vs nhé 

1/1.2+1/2.3+1/3.4+.........+1/14.15+1/15.16

=1-1/2+1/2-1/3+...+1/15-1/16

=1-1/16

=15/16  *k mk nha*

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{14.15}+\frac{1}{15.16}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{16}\)

\(=1-\frac{1}{16}\)

\(=\frac{16}{16}-\frac{1}{16}=\frac{15}{16}\)

tính hộ mình nha

\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right):x=\frac{3}{1.2}+\frac{3}{2.3}+\frac{3}{3.4}+...+\frac{3}{15.16}\)

\(\left(\frac{8}{16}+\frac{4}{16}+\frac{2}{16}+\frac{1}{16}\right).\frac{1}{x}=3.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{15.16}\right)\)

\(\frac{8+4+2+1}{16}.\frac{1}{x}=3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(\frac{15}{16}.\frac{1}{x}=3.\left(1-\frac{1}{16}\right)\)

\(\frac{15}{16}.\frac{1}{x}=3.\frac{15}{16}\)

=> \(\frac{1}{x}=3\)

=> \(x=\frac{1}{3}\)

*S=1-1/4+1/4-1/7+1/7-1/11+1/11-1/14+1/14-1/17

S=1-1/17=16/17

*M=2(1/1.2+1/2.3+...+1/15.16)

M=2(1-1/2+1/2-1/3+..+1/15-1/16)

M=2(1-1/16)

M=2.15/16

M=15/8

:w

\(S=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.11}+\frac{3}{11.14}+\frac{3}{14.17}\)

\(S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)

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

\(S=\frac{16}{17}\)

\(M=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{15.16}\)

\(M=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(M=2.\left(1-\frac{1}{16}\right)\)

\(M=2.\frac{15}{16}\)

\(=\frac{30}{16}=\frac{15}{8}\)

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

bài này là tính hả bạn ??

cau hỏi tương tự ko có mà!!!!!!!!!!!!!!!!!!!!!!!!!!!!

3C=1.2.3+2.3.(4-1)+3.4.(5-2)+...+2014.2015.(2016-2013)

3C=2014.2015.2016

C=2014.2015.2016:3

Ta có : S = 1.2 + 2.3 + 3.4 + ..... + 32.33

=> 3S = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ...... + 32.33.34

=> 3S = 32.33.34

=> S = \(\frac{32.33.34}{3}=11968\)