FunctionHard
Question
If f(1) = 1 and f(n + 1) = 2f(n) + 1 if n ≥ 1, then f(n) is equal to
Options
A.2n + 1
B.2n
C.2n - 1
D.2n-1 - 1
Solution
f(1) = 1 = 2 – 1
f(n + 1) = 2f(n) + 1
∴ f(1) = 1 = 2 - 1
f(n + 1) = 2f(n) + 1
Similarly f(n) = 2n - 1
f(n + 1) = 2f(n) + 1
∴ f(1) = 1 = 2 - 1
f(n + 1) = 2f(n) + 1
Similarly f(n) = 2n - 1
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