NCERT Class XI Mathematics - Binomial Theorem - Solutions

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Question : 14
Total: 36
Prove that
n
Σ
r=0
3r
n
Cr
= 4n
Solution:  
We have ,
n
Σ
r=0
3r
n
Cr
=
n
C30
+
n
C131
+
n
C232
+ ... +
n
Cn3n

= (1+3)n [Since
n
C0a0
+
n
C1a
+ ... +
n
Cnan
= (1+a)n] = 4n.
Hence proved.
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