GATE 2026 ST – Question 37

Calculus · Sequences and Series · 2 marks · Multiple choice

For x₁∈(0,4), define x_(n+1)=2−√(4−x_n). I:x_n→0. II:x_(n+1)/x_n→1/4. Which hold?

Only I correct
Only II correct
Both correct
Neither correct

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Show answer and explanation

Correct answer: (C) Both correct

Explanation

Rationalize to get x_(n+1)=x_n/[2+√(4−x_n)]. It stays positive and is less than x_n/2, so x_n→0. The same identity gives the ratio limit 1/(2+2)=1/4. Both true, **C**.

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