Register

JEST TCS 2025 | Section A (MCQ) | Question: 05

467 views

3 Answers

4 4 votes

As \(n \to \infty\), the sum \(\sum_{i=1}^n \frac{1}{i^2}\) converges to a constant (proof), so it is \(\Theta(1)\).  Hence
\[
S = n \cdot \Theta(1) = \Theta(n).
\]
(we use asymptotic analysis to understand behavior for large values of \(n\), i.e., as \(n \to \infty\))


 

Voting & Accepting an answer helps improve the community
← Previous · JEST TCS 2025 | Sect...Next → · JEST TCS 2025 | Sect...
← Previous in category · Stack Size in Binary...Next in category → · JEST TCS 2025 | Sect...
Position:
Show:

Related questions

1 1 vote
1 1 answer
341
341 views
Random Oracle asked Jul 2, 2025
341 views
JEST TCS 2025 | Section A (MCQ) | Question: 23
Let $f(n) := 2^n, g(n) := n$ and $h(n) :=$ $n^{log n}$. Which of the following statements is true$?$log $h(n) = O(g(n))$ and log $h(n) = \Omega$(log $f(n)).$$f(n)= O(g(n)...
1 1 vote
2 2 answers
310
310 views
Random Oracle asked Jul 3, 2025
310 views
JEST TCS 2025 | Section A (MCQ) | Question: 25
Let $S = \sum_{n\geq1} \dfrac{1}{n^2}$ and $A = \sum_{n\geq1}(-1)^{n+1}\dfrac{1}{n^2}$. Then which of the following statements is true?$S$ converges but $A$ does not conv...
0 0 votes
1 1 answer
272
272 views
Random Oracle asked Jul 3, 2025
272 views
JEST TCS 2025 | Section A (MCQ) | Question: 24
Let $a, b$ and $c$ denote regular expressions. Which of the following is an identity$?$None of the choices$a . (b + c) = (b + c) . a$$$c^* . a^* . b^* = c^* . b^* . a^*$$...
3 3 votes
1 1 answer
387
387 views
Random Oracle asked Jul 2, 2025
387 views
JEST TCS 2025 | Section A (MCQ) | Question: 22
Consider $n$ points equi-separated on a circle of radius one.Fix one of the points, and consider the product of the lengths of the chord from this point to all the other ...