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CGP EDU Academic Team
Published on: August 13, 2026
If (1 + x + x² +... + x p ) 6 = a 0 + a 1 x + a 2 x²+...+a 6p x 6p , then the value of :
[a 1 + 2a 2 + 3a 3 +.... + 6p a 6p ] is :
Text Solution
Verified by ExpertsThe correct answer is:
3
(3)
(1 + x + x 2 + .......+ x p ) n = a 0 + a 1 x + .....+ a np x np
Differentiating both side w.r.t. x
n(1 + x + x 2 + ........+ x p ) n – 1 (1 + 2x + ........+ px p – 1 ) = a 1 + 2a 2 x + .......+ np a np x np – 1
Now put x = 1
a 1 + 2a 2 + ..... + np a np = n(p + 1) n – 1 (1 + 2 + ........+ p) = 
, where n = 6
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