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

If (1+x)n=nr=0Crxr , then the value of the expression aC0+(a+b)C1+(a+2b)C2++(a+nb)Cn , equals

A
2nab(a+b)2n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2na2n+1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(2a+nb)2n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(2a+nb)2n1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D (2a+nb)2n1
Simplifying we get
a[nC0+nC1+nC2+....nCn]+b[nC1+2nC2+3nC3+...nnCn]
=a2n+b(d(1+x)ndx)x=1
=a2n+b(n(1+x)n1)x=1
=a2n+b(n2n1)
=(2a+bn)2n1

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