First slide

Algebra of real valued functions

Question

$f (1) = 1, n \geq 1 \Rightarrow f (n + 1) = 2 f (n) + 1$ then $f (n)$ =

Moderate

A

$2^{n + 1}$
B

$2^{n}$
C

$2^{n} - 1$
D

$2^{n - 1} - 1$

Solution

Put n = 1
$f (2) = 3 \Rightarrow f (2) = 2^{2} - 1 f (3) = 7 \Rightarrow f (3) = 2^{3} - 1 . . . . . f (n) = 2^{n} - 1$

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