Question
If A=1+r^a+r^ 2 a +r^ 3 a + and B =1+ r ^ b + r ^ 2 ~b + r ^ 3 ~b + , then a b is equal to
BITSAT
Mathematics
Sequences and Series
2024
BITSAT 2024 (Memory Based Paper 2)
BITSAT Mathematics Question (2024) — Solution
Options
- A. _B(A)
- B. _ 1-B (1-A)
- C. _ B-1 B ( A-1 A )
- D. None of these
Answer
C. _ B-1 B ( A-1 A )
Step-by-step solution
A= 1 1-r^a 1-r^a= 1 A r^a=1- 1 A = A-1 A B= 1 1-r^b 1-r^b= 1 B r^b=1- 1 B = B-1 B a r= ( A-1 A ) and b r= ( B-1 B ) a b = ( A -1 ~A ) ( B -1 ~B ) = _ B -1 ~B ( ~A -1 ~A )
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