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

Let f:NR be a function satisfying the following conditions:
f(1)=1 and f(1)+2f(2)++nf(n)=n(n+1)f(n) for n2.
If f(1003)=1K, then K equals

A
1003
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2003
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2005
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2006
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D 2006
f(1)+2f(2)++nf(n)=n(n+1)f(n) for n2
[1]
Replacing n by n+1, we get
f(1)+2f(2)++nf(n)+(n+1)f(n+1)=(n+1)(n+2)f(n+1)
[2]
From [2][1], we get
(n+1)f(n+1)=(n+1)(n+2)f(n+1)nf(n)
f(n+1)=(n+2)f(n+1)nf(n)
(n+1)f(n+1)=nf(n)
Putting n=2,3,4,, we get
2f(2)=3f(3)=4f(4)==nf(n)
From [1],
f(1)+(n1)nf(n)=n(n+1)f(n)
f(1)=2nf(n)
f(n)=f(1)2n=12n
f(1003)=12006
K=2006

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
General Tips for Choosing Functions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon