Question #86d0b

1 Answer
Ratnaker Mehta
Dec 18, 2017

Please see the Explanation.

Explanation:

The Error is in computing #a_(n+1)-a_n.#

# a_(n+1)-a_n=(n+1)/n-n/(n-1),#

#={(n+1)(n-1)-n^2}/{n(n-1)},#

#={(n^2-1)-n^2}/{n(n-1)}.#

# :. a_(n+1)-a_n=-1/(n(n-1)).#

#rArr AA n in NN-{1}, a_(n+1)-a_n lt 0.#

# rArr AA n in NN-{1}, a_(n+1) lt a_n.#

Clearly, #a_n=n/(n-1)# is monotonically decreasing.

Related questions
Impact of this question
173 views around the world
You can reuse this answer
Creative Commons License