S=\(\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}\right)\)+\(\frac{1}{2}\left(\frac{1}{2.3}-\frac{1}{3.4}\right)\)+..............+\(\frac{1}{2}\left(\frac{1}{37.38}-\frac{1}{38.39}\right)\).1428+185.8

S=\(\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+........\frac{1}{37.38}-\frac{1}{38.39}\right).\)1428+185.8

S=\(\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{38.39}\right)\).1428+185.8

S=\(\frac{185}{741}\).1428+1480

S=1836,518219

Tổng quát : \(\frac{2}{(a-1)\cdot a\cdot(a+1)}=\frac{1}{a(a-1)}-\frac{1}{a(a+1)}\)

Ta có : \(2A=2\cdot(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{37\cdot38\cdot39})\cdot1428+185\cdot8\)

\(\Leftrightarrow2A=(\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+...+\frac{2}{37\cdot38\cdot39})\cdot1428+185\cdot8\)

\(\Leftrightarrow2A=[(\frac{1}{1\cdot2}-\frac{1}{2\cdot3})+(\frac{1}{2\cdot3}-\frac{1}{3\cdot4})+...+(\frac{1}{37\cdot38}+\frac{1}{38\cdot39})]\cdot1428+185\cdot8\)

\(\Leftrightarrow2A=(\frac{1}{1\cdot2}-\frac{1}{38\cdot39})\cdot1428+185\cdot8=\frac{541680}{247}\)

\(\Leftrightarrow A=\frac{541680}{494}=1096,518219\approx1096,5\)

Chúc bạn học tốt

A = ( 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + ... + 1/37.38.39 ) . 1428 + 185 . 8

A = 1/2( 2/1.2.3 + 2/2.3.4 + 2/3.4.5 + ... + 2/37.38.39 ) . 1428 + 185.8

A = 1/2( 1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + 1/3.4 - 1/4.5 + ... + 1/37.38 - 1/38.39 ) . 1428 + 185.8

A = 1/2( 1/1.2 - 1/38.39 ) . 1428 + 185.8

A = 1/2 . 370/741 . 1428 + 185.8

A = 185/741 . 1428 + 185 . 8 

A = 185 . 1428 : 741 + 185 . 8

A = 185 . 476/247 + 185 . 8

A = 185 ( 476 / 247 + 8 )

A = 185. 2452/247

A = 1836,518219

\(2A=2\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{37.38.39}\right).1428+1480\)

\(=\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{37.38.39}\right)\times1428+1480\)

\(=\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{37.38}-\frac{1}{38.39}\right)\times1428+1480\)

\(=\left(\frac{1}{1.2}-\frac{1}{38.39}\right)\times1428+1480\)

\(=\left(\frac{741}{1482}-\frac{1}{1482}\right)\times1428+1480\)

\(=\frac{740}{1482}\times1428+1480\)

\(=\frac{528360}{741}+1480\)

Vongola: Em tách đúng tuy nhiên A còn hạng tử đằng sau, em nhân 2 thì phải nhân cả hạng tử đó nữa. Tức là không phải 1480 mà là 2960 e nhé :)

uk sai thiệt

bai nay mik lam sai roi nha

      \(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{37.38.39}\right).1428+185.8\)

\(=\frac{2}{2}.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{37.38.39}\right).1428+185.8\)

\(=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{37.38.39}\right).1428+1480\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{37.38}-\frac{1}{38.39}\right).1428+1480\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{38.39}\right).1428+1480\)

\(\frac{1}{2}.\frac{370}{741}.1428+1480\)

\(=\frac{185}{741}.1428+1480\)

\(=356,52+1480=1836,52\)

chỗ\(\frac{185}{741}.1428\)mk làm tròn số lun á nha

mk ko chắc tính đúng hay sai nha nhưng cách làm thì kiểu vậy

\(\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{37.38}-\frac{1}{38.39}\right).1428+185.8\)

\(=\left(\frac{1}{2}-\frac{1}{1482}\right).1482+1840\)

\(=\frac{740}{1482}.1482+1840\)

\(=740+1840\)

\(=2580\)

rat muon nhung minh lm khong dc

xin lỗi vì mình mới học lớp 5

= (1 - 1/2 - 1/3 + 1/2 - 1/3 - 1/4 + 1/3 - 1/4 - 1/5 + ... + 1/37 - 1/38 - 1/39) . 1428 + 1480

= (1 - 1/39) . 1428 + 1480

= 38/39 . 1428 + 1480

= 54264/39 + 1480

= 37328/13

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{19.20.21}\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{19.20}-\frac{1}{20.21}\right)\)

\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{20.21}\right)\)

\(=\frac{1}{2}.\frac{209}{420}\)

\(=\frac{209}{840}\)

\(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{19\cdot20\cdot21}\)

\(=\frac{1}{2}\left(\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+...+\frac{2}{19\cdot20\cdot21}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{19\cdot20}-\frac{1}{20\cdot21}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{19\cdot21}\right)\)

bn tự lm tp

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{19.20.21}\)

\(=\frac{1}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{19.20.21}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+....+\frac{1}{19.20}-\frac{1}{20.21}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{20.21}\right)=\frac{1}{2}.\frac{209}{420}=\frac{209}{840}\)

\(C=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{998\cdot999\cdot1000}\)

\(C=\frac{1}{2}\left[\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+...+\frac{2}{998\cdot999\cdot1000}\right]\)

\(C=\frac{1}{2}\left[\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+...+\frac{1}{998\cdot999}-\frac{1}{999\cdot1000}\right]\)

\(C=\frac{1}{2}\left[\frac{1}{2}-\frac{1}{999\cdot1000}\right]\)

Tính nốt :v

Ta có

\(C=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{998\cdot999\cdot1000}\)

\(\Rightarrow2C=\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+...+\frac{2}{998\cdot999\cdot1000}\)

\(=\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{998\cdot999}-\frac{1}{999\cdot1000}\)

\(=\frac{1}{1\cdot2}-\frac{1}{999\cdot1000}\)

\(=\frac{1}{2}-\frac{1}{999000}\)

\(=\frac{499500}{999000}-\frac{1}{999000}\)

\(=\frac{499499}{999000}\)

\(\Rightarrow C=\frac{499499}{1998000}\)

đúng nha bạn nhớ k mik

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

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

\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{38.39}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{1482}\right)\)

\(=\frac{1}{2}.\left(\frac{741}{1482}-\frac{1}{1482}\right)\)

\(=\frac{1}{2}.\frac{740}{1482}\)

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

Chúc bạn học tốt !!! 

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

Ta có : 2A = 2/1.2.3 + 2/2.3.4 +...+ 2/37.38.39

         2A = 1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + ...+ 1/37.38 - 1/38.39

         2A = 1/1.2 - 1/38.39

         2A = 740/1482 = 370/741

           A= 370/741 . 1/2 =........

* Công thức : 

\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{6}\right)=\frac{1}{2}.\frac{2}{6}=\frac{1}{6}=\frac{1}{1.2.3}\)

( VD cho dễ hiểu )