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If
f(1)=1 and
f(n)=f(n-1)^(2)+n then find the value of
f(4).
Answer:

If $f(1)=1$ and $f(n)=f(n-1)^{2}+n$ then find the value of $f(4)$ . $\newline$ Answer:

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Evaluate expression when a complex numbers and a variable term is given

Full solution

Q. If

f(1)=1

and

f(n)=f(n-1)^{2}+n

then find the value of

f(4)

.

\newline

Answer:

Find $f(2)$ : Given $f(1) = 1$ , we need to find $f(4)$ using the recursive formula $f(n) = f(n-1)^{2} + n$ . First, we find $f(2)$ . $f(2) = f(2-1)^{2} + 2$ $f(2) = f(1)^{2} + 2$ $f(2) = 1^{2} + 2$ $f(2) = 1 + 2$ $f(2) = 3$
Find $f(3)$ : Next, we find $f(3)$ using the value of $f(2)$ .
$f(3) = f(3-1)^{2} + 3$
$f(3) = f(2)^{2} + 3$
$f(3) = 3^{2} + 3$
$f(3) = 9 + 3$
$f(3) = 12$
Find $f(4)$ : Finally, we find $f(4)$ using the value of $f(3)$ .
$f(4) = f(4-1)^{2} + 4$
$f(4) = f(3)^{2} + 4$
$f(4) = 12^{2} + 4$
$f(4) = 144 + 4$
$f(4) = 148$

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