If α,β  are roots of 375x2−25x−2=0  and Sn=αn+βn , then limn→ ∞ ∑r=1nSr  is

The given equation is 375x2−25x−2=0 α,β are the roots of the equation, thenSum of the roots : α+β=25375=115  andProduct of the roots : αβ=−2375Given that, Sn=αn+βn                     ∑r=1nSr=(α+α2+.....+αn)+(β+β2+....+βn)∴  limn→∞ ∑r=1nSr=(α+α2+..... to  ∞)+(β+β2+..... to  ∞)                     =α1−α+β1−β                 (∵α+α2+..... to  ∞=α1−α   β+β2+....... to  ∞=β1−β)                       =α−αβ+β−αβ(1−α)(1−β)=(α+β)−2αβ1−α−β+αβ                     =115+43751−115−2375=25+4375−25−2=29348=112