wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The larger of (2n+1)n and (2n−1)n+2nn is (Assume that n is a positive integer greater than 100).

A
(2n+1)n
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
(2n1)n+2nn
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Both are equal
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
None of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A (2n+1)n
Given (2n+1)n and (2n1)n+(2n)n
Let n=200
So, (401)200 and (399)200+(400)200
Consider, (401)200(399)200
=(400+1)200(4001)200
=[200C0+200C1(400)199+200C2(400)198+.....+1][200C0200C1(400)199+200C2(400)198+.....+1]
=2[200C1(400)199+200C3(400)197+....+200C199(400)]
=2.200(400)199+2.200[200C3(400)196+....+200C198(400)]
=(400)200+a positive number >(400)200
(401)200(399)200>(400)200
(401)200>(399)200+(400)200
Hence, (2n+1)n>(2n1)n+(2n)n

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Algebraic Identities
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon