Question
Let u n+1 = 2un +1, (n = 0, 1, 2,…) and u0 = 0. Then u10 would be nearest to: (CAT 1993)
Answer: Option A
:
A
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A
Ans: (a)
u n+1 = 2un + 1 (n = 0, 1, 2,…..)
Put n = 0, u1 = 1
n = 1, u2 = 3
n = 2, u3 = 7
n = 3, u4 = 15
n = 4, u5 = 31
Seeing the pattern it is clear that un = 2n – 1
Hence u10 = (2)10 – 1 = 1,023.
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