Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If f(x) = 
[2x + 4x 3 + ………. + 2nx 2n–1 ], (0 < x < 1) then 
is equal to -
A
– 
B
C
D
Text Solution
Verified by ExpertsThe correct answer is:
D
f(x) = 
2 [x+ 2x 3 + ……. + nx 2n–1 ], 0 < x < 1
= 
2x [1 + 2x 2 + ……… + nx 2n–2 ]
= 2x 
( given progression is A.G.P.)
f(x) = 
∴ 
= 
dx
1 – x 2 = t
2xdx = – dt
= – 
= 
+ c
= 
+ c
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