Quantcast
Channel: TrueShelf : Crowdsourcing Exercises and Puzzles in Mathematics and Computer Science - latest exercises
Browsing all 6 articles
Browse latest View live

Article 1

Evaluate the following summation> $\sum_{i=1}^n {i^{-1/2}}$

View Article



Basics of Induction

Prove the following using induction: 1. $\sum_{i=1}^{n}{i} = \frac{n(n+1)}{2}$. 2. $\sum_{i=1}^{n}{i}^2 = \frac{n(n+1)(2n+1}{6}$. 3. $\sum_{i=1}^{n}{i}^3 = {(\frac{n(n+1)}{2})}^2$. 4....

View Article

Summations and Combinations

Prove the following : 1. $$\sum_{k=0}^{\lfloor n/2\rfloor} (-1)^k {n-k \choose k} \cdot 2^{n-2k} = n + 1$$ 2. $$\sum_{k=0}^n {2k \choose k}{2n-2k \choose n-k} = 4^n$$ 3. $$\sum_{k=0}^{n} 2^k {n \choose...

View Article

Summations and Combinations

Prove the following : 1. $$\sum_{k=0}^{\lfloor n/2\rfloor} (-1)^k {n-k \choose k} \cdot 2^{n-2k} = n + 1$$ 2. $$\sum_{k=0}^n {2k \choose k}{2n-2k \choose n-k} = 4^n$$ 3. $$\sum_{k=0}^{n} 2^k {n \choose...

View Article

Article 1

Evaluate the following summation> $\sum_{i=1}^n {i^{-1/2}}$

View Article


Basics of Induction

Prove the following using induction: 1. $\sum_{i=1}^{n}{i} = \frac{n(n+1)}{2}$. 2. $\sum_{i=1}^{n}{i}^2 = \frac{n(n+1)(2n+1}{6}$. 3. $\sum_{i=1}^{n}{i}^3 = {(\frac{n(n+1)}{2})}^2$. 4....

View Article
Browsing all 6 articles
Browse latest View live




Latest Images