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

If Cn is the coefficient of xn in the expansion of (1+x)n then C1+2.C2+3.C3++n.Cn=

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

The correct option is D n.2n1
(1+xn)=nr=0Crxn= nC0x0+nC1x+nC2x2+.....+nCnxn
Now,(1+xn)=C0+C1x+C2x2+.....+Cnxn ..(1)
Differentiating (1) w.r.t x
n(1+x)n1=C1+2C2x+.....+nCnxn1 ..(2)
put x=1 and get,
n2n1=C1+2C2+.....+nCn
C1+2C2+.....+nCn=n.2n1

flag
Suggest Corrections
thumbs-up
1
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