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

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

then find the value of

f(4)

.

\newline

Answer:

Calculate $f(2)$ : Given $f(1) = 2$ , we need to find $f(2)$ using the recursive formula $f(n) = f(n-1)^{2} + 1$ . $f(2) = f(1)^{2} + 1 = 2^2 + 1 = 4 + 1 = 5$ .
Calculate $f(3)$ : Now, we find $f(3)$ using the value of $f(2)$ we just calculated. $f(3) = f(2)^{2} + 1 = 5^2 + 1 = 25 + 1 = 26$ .
Calculate $f(4)$ : Finally, we find $f(4)$ using the value of $f(3)$ . $f(4) = f(3)^{2} + 1 = 26^{2} + 1 = 676 + 1 = 677$ .

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