Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The coefficient of x n in the expansion of 
is -
A
(2 n+2 – 3 n+3 + 1)
B
(3 n+2 – 2 n+3 + 1)
C
(2 n+3 – 3 n+2 + 1)
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
B
We have, 
= 
[By resolving into partial fractions]
= 
(1 – x) –1 –4 (1 – 2x) –1 + 
(1 – 3x) –1
= 
[1 + x + x 2 + …. + x n +….] – 4 [1 + 2x + (2x) 2 + ….. + (2x) n + ….] + 
[1 + (3x) + (3x) 2 + ….. + (3x) n + …..]
∴ Coefficient of x n = 
[1 – 8.2 n + 9.3 n ]
= 
[1 – 2 n+3 + 3 n+2 ].
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