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
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
tysm
