UP TGT Mathematics Real Analysis Test Series - Part 5
If a sequence (a_n) converges to L, then any shift sequence b_n = a_(n+k) for fixed k in N converges to:
Type: MCQ • Marks: 1
If a sequence (a_n) converges to L, then any shift sequence b_n = a_(n+k) for fixed k in N converges to:
Options
A. L + k
B. L / k
C. L
D. k * L
Explanation
Correct Answer: Option 3 (L). Limits in R are unique. Sum, product, and quotient rules hold. Cauchy's first/second limit theorems and Sandwich theorem provide useful tools for limit calculation.
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