A = 1/10 + 1/15 + 1/21 + ....+ 1/120

= 2/20 + 2/30 + 2/42 +....+ 2/240

= 2/4x5 + 2/5x6 + 2/6x7 + ...+ 2/15x16

= 2 x ( 1/4x5 + 1/5x6 + 1/6x7 +...+ 1/15x16)

=2 x ( 1/4 - 1/5 + 1/5 - 1/6 +1/6 - 1/7 + .....+ 1/15 - 1/16 )

= 2 x ( 1/4 - 1/16 )

= 2 x ( 4/16 - 1/16 )

= 2 x 3/16

= 6/16

= 3/8

tk nhé

Đợi duyệt nhé 

A=\(2.\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+......+\frac{1}{240}\right)\)

A=\(2.\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{15.16}\right)\)

A=\(2.\left(\frac{1}{4.}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+.......+\frac{1}{15}-\frac{1}{16}\right)\)

A=\(2.\left(\frac{1}{4}-\frac{1}{16}\right)\)

A=\(2.\left(\frac{4}{16}-\frac{1}{16}\right)\)

\(A=2.\frac{3}{16}\)

\(A=\frac{3}{8}\)

\(Vay\) \(A=\frac{3}{8}\)

=2

y = 1/10 + 1/15 + 1/21 + ... + 1/120

1/2y = 1/20 + 1/30 + 1/42 + ... + 1/240

1/2y = 1/4x5 + 1/5x6 + 1/6x7 + ... + 1/15x16

1/2y = 1/4 -1/5 + 1/5 - 1/6 + 1/6 -1/7 + ... +1/15 -1/16

1/2y = 1/4 - 1/16

1/2y = 3/16

y = 3/16 : 1/2

y = 3/16 x 2

y= 3/8

y=1/10 + 1/15 + 1/21 + ... + 1/120 (1)

Nhân cả 2 vế của đẳng thức (1) với 1/2 ta được:

1/2y=1/2.(1/10+1/15+1/21+...+1/120)

1/2y=1/20+1/30+1/42+...+1/240

1/2y=1/4.5+1/5.6+1/6.7+...+1/15.16

1/2y=1/4-1/5+1/5-1/6+1/6-1/7+...+1/15-1/16

1/2y=1/4-1/16

1/2y=4/16-1/16

1/2y=3/16

y=3/16:1/2

y=3/8

Vậy tổng dãy số trên bằng 3/8

Chúc bạn học tốt  Nguyễn Minh Hiếu

\(C=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}=2\times\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right)\)

\(C=2\times\left(\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+...+\frac{1}{15\times16}\right)\)

\(C=2\times\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)=2\times\left(\frac{1}{4}-\frac{1}{16}\right)=\frac{3}{8}\)

c = 2/20 + 2/30 +2/42 + ... 2 /240

=2/4.5 +2/5.6 + 2/6.7 + ... +1/15.16

=2. (1/4.5 + 1/5.6 + 1/6.7 +...+1/15.16)

= 2.(1/4-1/5+1/5-...-1/16)

=2.(1/4-1/6)=2.3/16=3/8.

ghi nho dau cham la dau nhan

\(S=\frac{2}{20}+\frac{2}{30}+...+\frac{2}{240}\)

\(=2\left(\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{15.16}\right)\)

\(=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(=2\left(\frac{1}{4}-\frac{1}{16}\right)\)

\(=2\times\frac{3}{16}\)

\(=\frac{3}{8}\)