Exercises
Multiple Choice
Articles
Open Problems
Login
Search
0
Undergraduate
By
Shiva Kintali
on May 31, 2013 | Updated Dec. 6, 2017
Evaluate the following summation
\(\sum_{i=1}^n {i^{-1/2}}\)
Mathematics
Discrete Mathematics
asymptotic analysis
summation
Post an answer
Cancel
Publish answer
Related Content
0
Undergraduate
By
Shiva Kintali
on Sept. 28, 2013 | Updated Jan. 4, 2018
Asymptotic Summations
Prove the following : \(\sum_{i=1}^{n} \frac{\log i}{i} = \Theta ((\log n)^2)\) \( \sum_{i=0}^{n} |\sin(i)| = \Theta(n)\) where \(i\) is in radians.
Mathematics
Discrete Mathematics
asymptotic analysis
0
High School
By
Shiva Kintali
on June 27, 2013 | Updated Jan. 4, 2018
Basics of Induction
Prove the following using induction: \(\sum_{i=1}^{n}{i} = \frac{n(n+1)}{2}\). \(\sum_{i=1}^{n}{i}^2 = \frac{n(n+1)(2n+1}{6}\). \(\sum_{i=1}^{n}{i}^3 = {(\frac{n(n+1)}{2})}^2\). …
Mathematics
Discrete Mathematics
induction
summation
0
High School
By
Shiva Kintali
on June 27, 2013 | Updated Jan. 4, 2018
Basics of Induction
Prove the following using induction: \(\sum_{i=1}^{n}{i} = \frac{n(n+1)}{2}\). \(\sum_{i=1}^{n}{i}^2 = \frac{n(n+1)(2n+1}{6}\). \(\sum_{i=1}^{n}{i}^3 = {(\frac{n(n+1)}{2})}^2\). …
Mathematics
Discrete Mathematics
induction
summation
1
Undergraduate
By
Shiva Kintali
on Sept. 27, 2013 | Updated Jan. 4, 2018
Fibonacci numbers and Induction
The Fibonacci numbers, \(F_0, F_1, F_2, \dots\) , are defined recursively by the equations \(F_0 = 0\), \(F_1 = 1\), and \(F_n = F_{n-1} + F_{n-2},\) for \(n > 1\). Prove that …
Mathematics
Discrete Mathematics
fibonacci
induction
tiling
1
Undergraduate
By
Shiva Kintali
on Sept. 27, 2013 | Updated Jan. 4, 2018
Fibonacci numbers and Induction
The Fibonacci numbers, \(F_0, F_1, F_2, \dots\) , are defined recursively by the equations \(F_0 = 0\), \(F_1 = 1\), and \(F_n = F_{n-1} + F_{n-2},\) for \(n > 1\). Prove that …
Mathematics
Discrete Mathematics
fibonacci
induction
tiling
1
Undergraduate
By
Shiva Kintali
on Sept. 27, 2013 | Updated Jan. 4, 2018
Fibonacci numbers and Induction
The Fibonacci numbers, \(F_0, F_1, F_2, \dots\) , are defined recursively by the equations \(F_0 = 0\), \(F_1 = 1\), and \(F_n = F_{n-1} + F_{n-2},\) for \(n > 1\). Prove that …
Mathematics
Discrete Mathematics
fibonacci
induction
tiling
0
Undergraduate
By
Shiva Kintali
on Sept. 28, 2013 | Updated Jan. 4, 2018
Summations and Combinations
Prove the following : \(\sum_{k=0}^{\lfloor n/2\rfloor} (-1)^k {n-k \choose k} \cdot 2^{n-2k} = n + 1\) \(\sum_{k=0}^n {2k \choose k}{2n-2k \choose n-k} = 4^n\) …
Mathematics
Combinatorics
n choose k
summation
0
Undergraduate
By
Vibhav Pant
on March 4, 2014 | Updated Dec. 6, 2017
Prove $\sum_{z=0}^{\infty}(\zeta(z)-1)=1$
Riemann's zeta function \(\zeta(z)\) is defined as \(\zeta(z)=1+\frac{1}{2^z}+\frac{1}{3^z}+\cdots=\sum_{k=0}^{\infty}\frac{1}{k^z}\) Prove that \(\sum_{z=0}^{\infty}(\zeta(z)-1)=1\)
Mathematics
Discrete Mathematics
sums
0
Undergraduate
By
Shiva Kintali
on May 31, 2013 | Updated Dec. 6, 2017
Let \(b > 1\). Then \(\log_b((n^2)!)\) is
Mathematics
asymptotic analysis
1
Undergraduate
By
Shiva Kintali
on Sept. 30, 2013 | Updated Jan. 4, 2018
Friends and Parties
Show that at a party of \(n\) people, there are two people who have the same number of friends in the party. Assume that friendship is symmetric. There are \(2n\) people at a party. Each person has…
Mathematics
Discrete Mathematics
counting
pigeonhole principle
icon
Sign In or Sign Up
icon
Invite Friends
Post Something
x
Select What You'd Like To Post
POST AN ARTICLE
POST AN OPEN PROBLEM
POST AN EXERCISE
POST A MULTIPLE-CHOICE QUESTION
Content Types
Articles
Open Problems
Exercises
Multiple-Choice Questions
Levels
High school
Undergraduate
Graduate
Subjects
Mathematics
Computer Science
Puzzles
Optimization
Trending tags
asymptotic analysis
summation
high probability
random graphs
cycle
path
counting
jee
jee 2016
jee advanced
Topics
Algebra
Algorithms
Approximation Algorithms
Calculus
Combinatorial Optimization
Combinatorics
Complexity Theory
Data Structures
Discrete Mathematics
Game Theory
Geometry
Graph Theory
Linear Algebra
Linear Programming
Logic
Mathematical Analysis
Mathematics
Matrix Theory
Number Theory
Optimization
Probability
Programming
Puzzles
Randomized Algorithms
Real Analysis
Trigonometry
×