S=2/3.7+2/7.1+2/11.15+...+2/95.99

S = \(\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{7}\right)+\frac{1}{2}.\left(\frac{1}{7}-\frac{1}{11}\right)+\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{15}\right)+...+\frac{1}{2}.\left(\frac{1}{95}-\frac{1}{99}\right)\)

S = \(\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{95}-\frac{1}{99}\right)\)

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

S = \(\frac{1}{2}.\frac{32}{99}\)

S = \(\frac{16}{99}\)

M=1/2+1/6+1/12+1/20+..+1/110

M = \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{10.11}\)

M = \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)

M = \(1-\frac{1}{11}\)

M = \(\frac{10}{11}\)

=1/1*2+1/2*3+1/3*4+...+1*10*11+1/11*12=1-1/2+1/2-1/3+1/3-1/4+...+1/10-1/11+1/11-1/12

=1-1/12=11/12.

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{110}+\frac{1}{132}\)

\(=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{10\times11}+\frac{1}{11\times12}\)

\(=1-\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{11}+\frac{1}{12}\)

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

\(=\frac{11}{12}\)

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}+\frac{1}{132}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}+\frac{1}{11.12}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)

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

\(=\frac{11}{12}\)

k mình nha ! Chúc bạn học giỏi ! ^_^

số số hạng từ 1 đến 144 là : 144 ( số )

Tổng dãy số là :

( 1 + 144 ) X 144 : 2 = 11088 

a, 1+2+3+5+8+...+144

Nhận xét: Ta thấy trong tổng trên kể từ số thứ 3 trở đi thì số liền sau bằng tổng của 2 số liền trước.

"3=2+1;5=3+2;8=5+3;..."

Vậy tổng được viết đầy đủ là:

1+2+3+5+8+13+21+34+55+89+144

Ta tính tổng là: 1+2+3+5+8+13+21+34+55+89+144=365

Còn b,c thì ko biết

c, 2 + 6 + 12 + 20 + ... + 110 

Đặt A = 2 + 6 + 12 + 20 + ... + 110

A = 1.2 + 2.3 + 3.4 + 4.5 + .... + 10.11

3A = 1.2.3 + 2.3.3 + 3.4.3 + 4.5.3 + ... + 10.11.3

3A = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + 4.5.(6 - 3) + ... + 10.11.(12 - 9) 

3A = 1.2.3 - 2.3.4 + 3.4.5 - 4.5.6 + ....- 10.11.12 

3A = 10.11.12

A = 10.11.12 : 3

A = 440 

\(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{110}\)
\(=\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{10.11}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\)
\(=1-\dfrac{1}{11}\)
\(=\dfrac{10}{11}\)

\(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{110}\\ =\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{10.11}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\\ =1-\dfrac{1}{11}=\dfrac{10}{11}\)

\(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{110}\\ =\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{10.11}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\\ =1-\dfrac{1}{11}\\ =\dfrac{10}{11}\)

\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+....+\dfrac{1}{110}\)

\(=\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+....+\dfrac{1}{10\times11}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+....+\dfrac{1}{10}-\dfrac{1}{11}\)

\(=1-\dfrac{1}{11}=\dfrac{10}{11}\)

B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + ... + 1/110

B = 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + .... + 1/10.110

B = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/10 - 1/11

B = 1 - 1/11

B = 10/11

 B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + .... + 1/110

=1/1x2 + 1/2x3 + 1/ 3x4 + 1/4x5 + 1/5 x6 + 1/ 6x 7 +.....+ 1/10 x11

=1-1/2 + 1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7 +......+ 1/10 - 1/11

= 1 + (1/2-1/2)+(1/3-1/3)+(1/4-1/4)+(1/5-1/5)+(1/6-1/6)+.....+(1/10-1/10)-1/11

= 1- 1/11=10/11

Vậy B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + .... + 1/110 = 10/11

cho mình hoi : 1/2 +1/6 +1/12 +1/30 +.....+1/110

cảm ơn nhé

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+..........+\frac{1}{132}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+..........+\frac{1}{11.12}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...........+\frac{1}{11}-\frac{1}{12}\)

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

\(=\frac{11}{12}\)

bài này hóc búa thật

hơi khó 5 chút

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{110}=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{10.11}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)

\(=\frac{1}{2}-\frac{1}{11}\)

\(\frac{9}{22}\)

Hồ Thu Giang làm đúng ròi

Đề sai phải không bạn, phải là\(...+\frac{1}{90}+\frac{1}{110}\)chứ