若n+1=20122+20132,则2n+1=_.

问题描述:

若n+1=20122+20132,则

2n+1
=______.

∵n+1=20122+20132
∴n=20122+20132-1,
∴2n=2×20122+2×20132-2,

2n+1
=
20122+2×20132−2+1
=
20122+2×(2012+1)2−2+1
=
20122+2×(20122+2×2012+1)−2+1
=
(2012×2+1) 2
=2012×2+1=4025;
故答案为:4025.