若n+1=20122+20132,则2n+1=_.
问题描述:
若n+1=20122+20132,则
=______.
2n+1
答
∵n+1=20122+20132,
∴n=20122+20132-1,
∴2n=2×20122+2×20132-2,
∴
=
2n+1
=
2×20122+2×20132−2+1
=
2×20122+2×(2012+1)2−2+1
=
2×20122+2×(20122+2×2012+1)−2+1
=2012×2+1=4025;
(2012×2+1) 2
故答案为:4025.