Follow the outline below and use mathematical induction toprove the Binomial Theorem:(a+b)^n=(n/a)^n+(_1^n)a^(n-1)b+n/2a^(n-2)b^2 +⋯+(n/(n-1))^(nb^(n-1)+n/n)b^n⋅ Becaus=(k/0)=((k+1)/0)(why)-and(k/k)=(k+1)(why?), substitute these results and ...
Follow the outline below and use mathematical induction to prove the Binomial Theorem:(a+b)^n=(pmatrix) n 0(pmatrix) a^n+(pmatrix) n 1(pmatrix) a^(n-1)b+(pmatrix) n 2(pmatrix) a^(n-2)b^2+⋯ +(pmatrix) n n-1(pmatrix) ab^(n-1)+(pmatrix) n n(pmatrix) b^n....
The mathematical proof technique of induction is used to prove that properties or rules are true for the natural numbers (positive whole numbers) . It generally involves two steps: The base step and the induction step. The base involves proving that the rule is true f...
We have to prove a standard limit. We will first expand the expression by binomial theorem. The rearrange the the expression and then apply the limits and we see that the limit is proved. Answer and Explanation:1 {eq}\text{applying the binomial theorem}\\left (1+\frac{1}{n} \...
This is a problem from Elementary Number Theory by David M. Burton. I was able to solve part (a)(a) by expanding (ax+by)2n−1(ax+by)2n−1 using binomial theorem and factoring. To solve part (b)(b), I used Bezout's theorem along with the following hint given in the book:...
Answer to: Prove that if m* (A△B) = 0, then m* (A) = m* (B). Hint: Note that A ⊆ B ∪ (A△B) By signing up,...
Class 12MATHSBINOMIAL THEOREMSimilar Questions Find the sum of 11!(n−1)!+13!(n−3)!+15!(n−5)!+..., View Solution The sum of the series 11!(n−1)!+13!(n−3)!+15!(n−5)!+…..+1(n−1)!1! is = (A) 1n!2n (B) 2nn! (C) 2n−1n! (D) 1n!2n−...
Prove by induction. ? n k = 0 ( k + 2 2 ) = ( n + 3 3 ) Prove that P(A|B) \leq P(A|A \cap B) Let X ? N(�, ?2 ). Find the values of � and ? such that P(|X| < 2) = 1/2. Prove or disprove that t...
Prove by induction. ? n k = 0 ( k + 2 2 ) = ( n + 3 3 ) prove that SSR = frac{( (SXY)^2)}{SXX} Prove that V (a X + b) = a^2 Std^2 with x on lower bottom. [Hint: With h (X) = a X + b, E [h (X)] = a m + b where m = E (X).]. Show that...