\(A=\frac{1}{1.3.5}+\frac{1}{3.5.7}+\frac{1}{5.7.9}+...+\frac{1}{95.97.99}\)

\(A=4.\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+\frac{1}{5.7}-\frac{1}{7.9}+...+\frac{1}{95.97}-\frac{1}{97.99}\right)\)

\(A=4.\left(\frac{1}{1.3}-\frac{1}{97.99}\right)\)

\(A=4.\frac{3200}{9603}=\frac{12800}{9603}\)

\(A=\frac{1}{1.3.5}+\frac{1}{3.5.7}+\frac{1}{5.7.9}+...+\frac{1}{95.97.99}\)

\(A=\frac{1}{4}.\left(\frac{1}{1.3.5}+\frac{1}{3.5.7}+\frac{1}{5.7.9}+...+\frac{1}{95.97.99}\right)\)

\(A=\frac{1}{4}.\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+\frac{1}{5.7}-\frac{1}{7.9}+...+\frac{1}{95.97}-\frac{1}{97.99}\right)\)

\(A=\frac{1}{4}.\left(\frac{1}{1.3}-\frac{1}{97.99}\right)\)

\(A=\frac{1}{4}.\frac{3200}{9603}\)

\(A=\frac{800}{9603}\)

Bài trc mik làm lộn :)))
~ Hok tốt ~
 

A = 1/4.( 4/1.3.5 + 4/3.5.7+ ....+ 4/95.97.99)

    = 1/4 .( 1/ 1.3 - 1/3.5 + 1/3.5 - 1/5.7 + .......+ 1/95.97 - 1/97.99)

   = 1/4( 1/1.3 - 1/97.99)

    = 1/4 . 9499/29397

đáp án là : 35/429

các pn thân iu ơi giúp mik với nha! chìu nay mik cần r!

https://www.youtube.com/watch?v=vNJ2wLqK7Mw

lên đây tham khảo nha

B = \(\frac{1}{1.3.5}+\frac{1}{3.5.7}+....+\frac{1}{95.97.99}\)

B = \(\frac{1}{4}.\left(\frac{5-1}{1.3.5}+\frac{7-3}{3.5.7}+...+\frac{99-95}{95.97.99}\right)\)

B = \(\frac{1}{4}.\left(\frac{5}{1.3.5}-\frac{1}{1.3.5}+\frac{7}{3.5.7}-\frac{3}{3.5.7}+...+\frac{99}{95.97.99}-\frac{95}{95.97.99}\right)\)

B = \(\frac{1}{4}.\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{95.97}-\frac{1}{97.99}\right)\)

B = \(\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{97.99}\right)\)

B = \(\frac{1}{4}.\frac{3200}{9603}\)

B = \(\frac{800}{9603}\)

mk ko viết đề nhé

C=1.3.5.8 + 3.5.7.8 + 5.7.9.8 + … + 95.97.99.8

C= 1.3.5(7 + 1) + 3.5.7(9 - 1) + 5.7.9(11 - 3) + … + 95.97.99(101 - 93)

C= 1.3.5.7 + 15 + 3.5.7.9 - 1.3.5.7 + 5.7.9.11 - 3.5.7.9 + … + 95.97.99.101 - 93.95.97.99

C= 15 + 95.97.99.101

=>C=\frac{15 + 95.97.99.101}{8}

1.3.5.8 + 3.5.7.8 + 5.7.9.8 + … + 95.97.99.8

= 1.3.5(7 + 1) + 3.5.7(9 - 1) + 5.7.9(11 - 3) + … + 95.97.99(101 - 93)

= 1.3.5.7 + 15 + 3.5.7.9 - 1.3.5.7 + 5.7.9.11 - 3.5.7.9 + … + 95.97.99.101 - 93.95.97.99

=15 + 95.97.99.101

=> A = \frac{15.95 + 97.99.101}{8}

\(A=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{1997.1999}-\frac{1}{1999.2001}\)

     \(=\frac{1}{1.3}-\frac{1}{1999.2001}\)

       Bạn tính kết quả nhé

Gọi B là biểu thức đã cho.
Dễ dàng chứng minh:

...
Ta có:
B