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

Find the sum of the infinite binomial series1+13+1336+133659+...

A
3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 3
For a binomial expansion, we can write as
We can write as
1+nx+n(n1)2x2...
Comparing coefficients, we get
nx=13 ...(i)
n(n1)2x2=16
x2n2nx2=13
n2x2nx2=nx ...from(i)
nx(nxx1)=0
13(13(x+1))=0
x+1=13
x=23 ...(ii)
Therefore n=12
Therefore the expression will be
(1+x)n
=(123)12
=3

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Sum of Infinite Terms of a GP
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon