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

If (1+x)n=nr=0Crxr
Prove that 22C01.2+23C12.3+......+2n+2Cn(n+1)(n+2) =?

Open in App
Solution

(1+x)n=nr=0crxr
(1+x)n=nr=0crxr [ By integrating both side ]
(1+x)n+1n+1=nr=0crxr+1r+1
1n+1(1+x)n+1=nr=0crr+1xr+1 [Again integration ]
1(n+1)(n+2)(1+x)n+2=nr=0cr(r+1)(r+1).xr+2
C01.2x2+C12.3.x3+......+Cn(n+1)(n+2).xn+2=(1+x)n+2(n+1)(n+2)
by putting x=2 the equation become
C01.222+C12.3.23+......+Cn(n+1)(n+2).2n+2=3n+2(n+1)(n+2)
3n+2(n+1)(n+2)
Hence, proved.


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