Question

Tính :

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

Answer 1

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

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

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

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

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

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

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

Answer 2

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 :)

Answer 3

uk sai thiệt

Answer 4

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

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

     \(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{2.4}+...+\frac{1}{37.38}-\frac{1}{38.39}\right)\)

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

     \(=\frac{1}{2}.\left(\frac{370}{741}\right).1428+185.8\)

     \(=\frac{185}{741}.1428+1480\)

      

Answer 5

Kết quả bằng 528360/741 + 1480 nha bạn!^^

Chúc bạn hok tốt =)) thấy đúng thì k cho mk nha!

Answer 6

528360/741+1480

Answer 7

Tổng quát: \(\frac{2}{\left(a-1\right).a.\left(a+1\right)}=\frac{1}{a\left(a-1\right)}-\frac{1}{a\left(a+1\right)}\)

Ta có:\(2A=2.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{37.38.39}\right).1428+185.8\)

\(\Leftrightarrow2A=\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+....+\frac{2}{37.38.39}\right).1428+185.8\)

\(\Leftrightarrow2A=\left[\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+...+\left(\frac{1}{37.38}-\frac{1}{38.39}\right)\right].1428+185.8\)

\(\Leftrightarrow2A=\left(\frac{1}{1.2}-\frac{1}{38.39}\right).1428+185.8=\frac{541680}{247}\)

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

Answer 8

2960 k mk nha mk k lại

Answer 9

Đây là đáp án:

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

Answer 10

A=( 1-1/2-1/3+1/2-1/3-1/4+...+1/37-1/38-/139).1428+185.8

A=(1-1/39).1428+185.8

A=38/39.1428+185.8

A=18088/13+1480

A=37328/13

Answer 11

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

A = 2/1.2.3+2/2.3.4+...+2/37.38.39

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

A  =( 1/1.2-1.38.39).1428+1428+185.8

( Các bước tiếp theo bạn tự giải nhé0