1) Đặt \(A=1.2+2.3+3.4+....+98.99\)

Ta có:\(3A=3.\left(1.2+2.3+3.4+....+98.99\right)\)

\(3A=1.2.3+2.3.3+3.4.3+....+98.99.3\)

\(3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+....+98.99.\left(100-97\right)\)

\(3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+....+98.99.100-97.98.99\)

\(3A=98.99.100\Rightarrow A=\frac{98.99.100}{3}=323400\)

Ta có:\(\frac{A.y}{1}=184800\Rightarrow y=184800:323400=\frac{4}{7}\)

2)Đặt \(A=\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{37.38.39}\right).1428+185,8\)

\(B=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+....+\frac{1}{37.38.39}\)

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

Ta có:

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

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

\(2B=\frac{1}{1.2}-\frac{1}{38.39}=\frac{370}{741}\Rightarrow B=\frac{370}{741}:2=\frac{185}{741}\)

Khi đó \(A=\frac{185}{741}.1428+185,8=...........\) (tự tính ra)

(*)số ko đẹp mấy

giup minh voi cac ban

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}=\frac{49}{50}\)

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)

=\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

=\(\frac{1}{1}-\frac{1}{50}=\frac{50}{50}-\frac{1}{50}=\frac{49}{50}\)

bài toán giải theo phương pháp khử liên tiếp (Toán nâng cao). Áp dụng công thức: \(\frac{a}{k.m}=\frac{a}{k}-\frac{a}{m}\)với a,k,m\(\in N\)

\(k< m;m-k=a\)

A=1-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+...+\(\frac{1}{49}\)-\(\frac{1}{50}\)

  = 1-\(\frac{1}{50}\)

  = \(\frac{49}{50}\)

ta có công thức tính tổng quát 1/[n(n+1)] = 1/n -1/(n+1) 
=> A=1/1.2+ 1/2.3+1/3.4+1/4.5+...+1/49.50 
=1/1 -1/2 +1/2 -1/3 +1/3-1/4+.......+1/49 -1/50 
= 1 -1/50 = 49/50 

Ai thấy đúng thì tk cho mk nhé 

= \(\frac{49}{50}\).

Đúng 100% luôn!

Chúc các bạn học giỏi.

Thêm đk \(a,b,c\ne0\)

Ta có: \(\frac{ab}{a+b}=\frac{1}{3}\Rightarrow\frac{a+b}{ab}=3\)

\(\frac{bc}{b+c}=\frac{1}{4}\Rightarrow\frac{bc}{b+c}=4\)

\(\frac{ca}{c+a}=\frac{1}{5}\Rightarrow\frac{c+a}{ca}=5\)

\(\Rightarrow\frac{a+b}{ab}+\frac{b+c}{bc}+\frac{c+a}{ca}=12\)

\(\Leftrightarrow\frac{1}{b}+\frac{1}{a}+\frac{1}{c}+\frac{1}{b}+\frac{1}{a}+\frac{1}{c}=12\)

\(\Leftrightarrow2\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)=12\)

\(\Leftrightarrow\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=6\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

\(=\frac{1}{1}-\frac{1}{50}\)

\(=\frac{49}{50}\)

1/1×2 + 1/2×3 + 1/3×4 + ... + 1/49×50

= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/49 - 1/50

= 1 - 1/50

= 49/50

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

\(=1-\frac{1}{50}\)

\(=\frac{49}{50}\)

k nha

hello

6/u

trrtu

\(B=\frac{10}{2.7}+\frac{10}{7.12}+...+\frac{10}{502.507}\)

\(B=2.\left(\frac{5}{2.7}+\frac{5}{7.12}+...+\frac{5}{502.507}\right)\)

\(B=2.\left(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+...+\frac{1}{502}-\frac{1}{507}\right)\)

\(B=2.\left(\frac{1}{2}-\frac{1}{507}\right)\)

\(B=2.\frac{505}{1014}\)
\(B=\frac{505}{507}\)