Question Number 104176 by Dwaipayan Shikari last updated on 19/Jul/20

Σ_(n=1) ^∞ (((n/(n+1)))^2 −(2/(n+1))−1)

Answered by OlafThorendsen last updated on 19/Jul/20

u_n  = ((n/(n+1)))^2 −(2/(n+1))−1  u_n  = −((4n+3)/((n+1)^2 ))  u_n  = −(4/(n+1))+(1/((n+1)^2 ))    Σ_(n=1() ^∞ (1/(n+1)^2 )) is convergent  Σ_(n=1) ^∞ (4/(n+1)) is divergent  ⇒Σ_(n=1) ^∞ u_n  is divergent  (sorry for my approximative english)