+0  
 
0
175
2
avatar

In an arithmetic sequence a1,a2,a3,...,We know a1=1 and an=1/n for some integer n>1
(a)What is the common difference of this arithmetic sequence, in terms of n?
(b) compute the value of an+1

 Feb 17, 2021
 #1
avatar+120129 
+2

The first few  terms are

1,1/2,1/3, 1/4, etc.

 

The  common difference is      

 

1/ (n + 1)    - 1 / n  = 

 

(n  -  (n + 1))                 -1

___________   =   ________

   n ( n + 1)               n^2  + n

 

 

an+1  =    1  / n    -     1  / ( n^2 + n)     =     ( n^2  + n  -  n)  / ( n * (n^2 +n))   = 

 

 n^2 / ( n^2 (n + 1))  = 

 

1/ n + 1

 

 

 

cool cool cool

 Feb 17, 2021
edited by CPhill  Feb 17, 2021
 #2
avatar
0

tysm

Guest Feb 26, 2021

14 Online Users

avatar
avatar