Published by:
CGP EDU Academic Team
Published on: August 13, 2026
f(x) = 
(2x + 4x 3 +……..+ 2 n x 2n–1 ) (0 < x < 1) then 
is equal to
A
log 
+ c
+ c
B
log 
+ c
+ c
D
log 
+ c None of these
+ c None of these
Text Solution
Verified by ExpertsThe correct answer is:
C
Solve series
s = 2x + 4x 3 +…+ 2 n x 2n–1 → Total term (n) → G.P.
s = 2(x) 
→ first term = 2x
→ C.R. = 2x 2
s = (2x) 
, 
x 2n → 0
f(x) = s = 
so 
dx put 1 – 2x 2 = t
– 4x dx = dt
2x dx = – 1/2 dt
= – 
= – 
log (t) + c
= – 
log (1 – 2x 2 ) + c
= log 
+ c
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