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

If $f(1)=2$ 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)=2

and

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

then find the value of

f(4)

.

\newline

Answer:

Find $f(2)$ : Given $f(1) = 2$ , we need to find $f(2)$ using the recursive formula $f(n) = f(n-1)^{2} + n$ .
$f(2) = f(2-1)^{2} + 2$
$f(2) = f(1)^{2} + 2$
$f(2) = 2^{2} + 2$
$f(2) = 4 + 2$
$f(2) = 6$
Find $f(3)$ : Now we have $f(2) = 6$ , we will find $f(3)$ using the recursive formula. $\newline$ $f(3) = f(3-1)^{2} + 3$ $\newline$ $f(3) = f(2)^{2} + 3$ $\newline$ $f(3) = 6^{2} + 3$ $\newline$ $f(3) = 36 + 3$ $\newline$ $f(3) = 39$
Find $f(4)$ : Having found $f(3) = 39$ , we will now find $f(4)$ using the recursive formula. $\newline$ $f(4) = f(4-1)^{2} + 4$ $\newline$ $f(4) = f(3)^{2} + 4$ $\newline$ $f(4) = 39^{2} + 4$ $\newline$ $f(4) = 1521 + 4$ $\newline$ $f(4) = 1525$

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