Question
Question: If [x] denotes the greatest integer less than or equal to x and F = R – [R] where \(R = \left( 5\sqr...
If [x] denotes the greatest integer less than or equal to x and F = R – [R] where R=(55+11)2n+1then RF is equal to –
A
42n+1
B
42n
C
42n–1
D
None of these
Answer
42n+1
Explanation
Solution
Let G = (55−11)2n+1, then 0 < G < 1,
Now, R – G = (55+11)2n+1 – (55−11)2n+1
= 2 [2n+1C1(55)2n(11)+.....]
= an even integer
Ž F – G = 0
Ž F = G
RF = RG = (55+11)2n+1(55−11)2n+1
= 42n+1