\(A=\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+...+\frac{1}{36\times37\times38}+\frac{1}{37\times38\times39}\)

\(2A=\frac{2}{1\times2\times3}+\frac{2}{2\times3\times4}+\frac{2}{3\times4\times5}+...+\frac{2}{36\times37\times38}+\frac{2}{37\times38\times39}\)

\(2A=\frac{1}{1\times2}-\frac{1}{2\times3}+\frac{1}{2\times3}-\frac{1}{3\times4}+...+\frac{1}{37\times38}-\frac{1}{38\times39}\)

\(2A=\frac{1}{1\times2}-\frac{1}{38\times39}\)

\(2A=\frac{741}{1482}-\frac{1}{1482}\)

\(2A=\frac{370}{741}\)

\(A=\frac{370}{741}:2=\frac{185}{741}\)

\(=\frac{1}{1\times2}-\frac{1}{2\times3}+\frac{1}{2\times3}-\frac{1}{3\times4}+...+\frac{1}{37\times38}-\frac{1}{38\times39}\)

\(=\frac{1}{1\times2}-\frac{1}{38\times39}=\frac{1}{2}-\frac{1}{1482}=\frac{370}{741}\)

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{36.37.37}\)

\(=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{36.37.38}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{36.37}-\frac{1}{37.38}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{37.38}\right)\)

\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{1406}\right)\)

\(=\frac{1}{2}.\frac{351}{703}\)

\(=\frac{351}{1046}\)

\(\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....-\frac{1}{36}+\frac{1}{37}-\frac{1}{38}+\frac{1}{38}-\frac{1}{39}\)

=\(\frac{1}{1}-\frac{1}{39}\)

=\(\frac{38}{39}\)

đảm bảo đúng

\(A=\frac{370}{741}\)

A=\(\frac{370}{741}\)

A = 2/1x2x3 + 2/2x3x4 + 2/3x4x5 + ... + 2/36x37x38 + 2/37x38x39

A = 1/1x2 - 1/2x3 + 1/2x3 - 1/3x4 + 1/3x4 - 1/4x5 + ...+ 1/36x37 - 1/37x38 + 1/37x38 - 1/38x39

A = 1/2 - 1/38x39

A = 370/741

Tớ ko chắc là đúng đâu

bài 

Nguyễn Hà Thương sai chưa chia 2

\(2C=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{39-37}{37.38.39}\)
\(2C=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{37.38}-\frac{1}{38.39}\)
\(2C=\frac{1}{1.2}-\frac{1}{38.39}\)
\(C=\frac{617}{1482}\)

\(3D=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\)
\(3D-D=1-\frac{1}{3^8}\)
\(D=\frac{1}{2}-\frac{1}{2.3^8}\)

Ta có:\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+....+\frac{1}{37.38}-\frac{1}{38.39}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{38.39}\right)\)

b,\(D=\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^8}\)

\(\Rightarrow3D=1+\frac{1}{3}+\frac{1}{3^2}+.....+\frac{1}{3^7}\)

\(\Rightarrow2D=1-\frac{1}{3^8}\)

\(\Rightarrow D=\frac{3^8-1}{3^8}:2\)

Ta có : 

\(C=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{4.5.6}+...+\frac{1}{37.38.39}\)

\(2C=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{37.38.39}\)

\(2C=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{37.38}-\frac{1}{38.39}\)

\(2C=\frac{1}{2}-\frac{1}{38.39}\)

\(C=\frac{\frac{1}{2}-\frac{1}{38.39}}{2}\)

\(C=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{38.39}\right)\)

\(C=\frac{1}{2}.\frac{370}{741}\)

\(C=\frac{185}{741}\)

=1/1.2.3+1/2.3.4+....+1/37.38.39

=1/1.2-1/2.3+1/2.3-1/3.4+...+1/37.38-1/38.39

=1/1.2-1/38.39

=1/2-1/38.39

=370/7410

bạn ơi, mình dùng dấu nhân bằng dấu chấm bạn nha(  còn dấu ... thì bình thường)

mình chắc chắn đúng. cái này bạn học toán phần nâng cao lớp 5 dạng sai phân.

chúc bạn học giỏi

2/1×2×3 + 2/2×3×4 + 2/3×4×5 + ... + 2/36×37×38 + 2/37×38×39

= 1/1×2 - 1/2×3 + 1/2×3 - 1/3×4 + 1/3×4 - 1/4×5 + ... + 1/36×37 - 1/37×38 + 1/37×38 - 1/38×39

= 1/1×2 - 1/38×39

= 1/2 - 1/1482

= 370/741

\(\text{Ta có: }\) \(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}+....+\frac{1}{37.38}-\frac{1}{38.39}\)

                  \(=\frac{1}{2}-\frac{1}{38.39}\)

                  \(=\frac{1}{2}-\frac{1}{1482}\)

                  \(=\frac{370}{741}\)

\(S=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{98\cdot99\cdot100}\)

\(S=\frac{3-1}{1\cdot2\cdot3}+\frac{4-2}{2\cdot3\cdot4}+...+\frac{100-98}{98\cdot99\cdot100}\)

\(2S=\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+...+\frac{2}{98\cdot99\cdot100}\)

\(2S=\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+...+\frac{1}{98\cdot99}-\frac{1}{99\cdot100}\)

\(2S=\frac{1}{1\cdot2}-\frac{1}{99\cdot100}\)

\(\Rightarrow S=\left(\frac{1}{1\cdot2}-\frac{1}{99\cdot100}\right)\div2=\frac{4949}{19800}\)

Ta có:

Sx3 = 3/1 x ( 1/1x2x3 + 1/2x3x4 + .... + 1/98x99x100 )

Sx3 = 3/1x2x3 + 3/2x3x4 + .... + 3/98x99x100

Sx3 = (1/2 x 1/2x3) + (1/2x3 x 1/3x4) + ... + (1/98x99 + 1/99x100)

S     = (1/2 x 1/98x99) :3

S      = 1/59400

Mk ko quen vt p/s nên vt thế này cho nhanh sorry

S=(1/2 x 1/89x99):3 

S=1/59400

đ/s:.......

vậ x=