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I was solving a binomial summation problem, and I got $^{40}C_{12}$ as the answer. Now, the question demands to find the remainder when it is divided by $7$....
Asked on 12/10/2021 by yash bhatia
2 answerI have to show that for some group it is abelian iff $x • (y • x^{−1}) = y$.This is what I did:Starting with the given statement...
Asked on 12/10/2021 by cheese12345
2 answerHow do I prove the following?- $sqrt{2}sum_{n=0}^{infty} frac{Gamma(2n+1/2)(-at)^n}{n!Gamma(n+1/2)}$=$frac{sqrt{1+sqrt{1+4at}}}{sqrt{1+4at}}$. I think the way to obtain the right-hand side is to show that the summation expansion of left expression can...
Asked on 12/10/2021 by Paranoid
1 answerConsider the two independent random variables $X$ and $Y$. Assume both are uniformly distributed on $[0,1]$. I want to calculate the probability that $X$ lies between...
Asked on 12/10/2021 by sottoj
1 answerConsider the following sequences:A : (4, 7, 10, 13, 16, 19, ...) ..+3B : (3, 10, 17, 24, 31, 38, ...) ..+7C : (8, 19, 30,...
Asked on 12/10/2021 by Billy senders
1 answerConsider the following function:$$varphi(m) = begin{cases} 1 & m = 1 vee bigg( m= 2^n3^k wedge varphi(k)= 1 bigg)\ 0 & o.w.end{cases}$$So $varphi$ evaluates whether an...
Asked on 12/10/2021 by user6767509
2 answerLet $x_iin(0,1]$ for all $i$. Are the following true, and if so is there a easy proof or citation.$prod_{i=1}^infty x_i = e^{sum_{i=1}^infty log x_i}$ always holds (if...
Asked on 12/10/2021 by LCE
1 answerThis set appears in an exercise of the course Introduction to Mathematical Thinking, by Dr.Keith Devlin$A$=${nin Bbb Nlvert (n>1)wedge (forall x,yin Bbb N)[(xy=n)implies (x=1lor y=1)]}$Although this is the...
Asked on 12/10/2021
2 answerI was reading permutation without repetition which says that In a pool if $16$ balls there are $N!$ possibilities, which is,$16 × 15 × 14 ×...
Asked on 12/10/2021 by mahesh87
1 answerLet us consider the codes $C[n,k]$ where $n=31$ and $k=5$ and base field $mathbb{F}_2$. I know there are ${31}choose{k}$ divisors of $x^ {31}-1$ of...
Asked on 12/10/2021
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