Part BCSIR NET June 2025the-limit-must-satisfy-the-fixed-point-equation

The limit must satisfy the fixed point equation

Let $f : R$ \ $Q \to R$ \ $Q$ be the function defined as f(x) = (3x + 2)/(4x + 3). Let $x_{1} \in R$ \ $Q$ . For n ≥ 1, define $x_{n}$ ₊ $_{1} = f (x_{n})$ . Suppose that the sequence $(x_{n})_{n} \geq_{1}$ converges to a real number $ℓ$ . Which of the following statements is true?

A.If $ℓ$ is positive, then $ℓ = 3 /2$ .
B.If $ℓ$ is positive, then $ℓ = 1/ 2$ .✓
C.If $ℓ$ is negative, then $ℓ = - 3 /2$ .
D.If $ℓ$ is negative, then $ℓ = - 1/2$ .

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: aₙ^{1/n} → L ⇒ aₙ₊₁/aₙ → L

The limit must satisfy the fixed point equation

More on this topic