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1. ### Use Induction to prove?

...1 maybe > 1). 2. Assume it to be true for a generic term n. 3. Show that if it works for n it...2/2]^2 = 1 hence true for n = 1 assume true for n: ∑ j^3 = [n(n+1)/2]^2 for i = 1 to n for n+1 ∑ j^3...

1 Answers · Science & Mathematics · 11/10/2009

2. ### Prove by math induction that n.1+(n-1).2+(n-2).3+....+2(n-1)+1.n=n.(n+1).(n+2)/6?

general term is a[j] = (n+1-j)*j; s(n) =Σa[j], where j=1 until n; ♠check n=2...3+1)*(3+2)/6 =10; good! ♣ s(n+1) =Σ ((n+1) +1 –j)*j = Σ ((n+1 -j +1)*j {j=1 until n+1} = = Σ((n+1 –j)*j +j...

2 Answers · Science & Mathematics · 04/09/2008

3. ### Prove that |kA| = k^n |A|?

... that, if you have a matrix of the form A = [a_1...ca_i + db_i...a_n] where the a_j's (and ca_i + db_i) stand for the columns of the matrix A and c...

4 Answers · Science & Mathematics · 11/08/2008

4. ### Show that S is denumerable?

1) (1, j) is a member of S for each j from N ==> cardinality of S is at least as big as the cardinality of N...

1 Answers · Science & Mathematics · 21/07/2010

5. ### Find the function and simplify?

n(j(x)) = 5/((-6 + 20/(-2 + x)) (-2 + x)) = 5/(32 - 6 x)

1 Answers · Science & Mathematics · 30/07/2015

6. ### Power Sets finding each of the following?

...j ∈ Z, m=3j } and B = {n ∈ Z ; ∃ k ∈ Z, n=7k} then A n B = {m ∈ Z ; ∃ j ∈ Z, m = 21j } 2. P({4,5,6}) = { {4,5;6} , { 4,5 } , { 4,6 } , { 5,6...

1 Answers · Science & Mathematics · 22/12/2013

7. ### Number Theory Proof Help Please?

...list of all a[k] ^ j will still be completely distinct from the list n[k] and therefore (a^j, n) = (a, n) = 1

2 Answers · Science & Mathematics · 31/01/2012

8. ### Proof if p is prime and p | a_1a_2a_3...a_n, then p | a_ j for some j, 1 < j < n. Use induction?

...proposition. Suppose this is true for n = k. Given p | a_1a_2a_3...a_k a_(k+1) = (a_1a_2a_3...a_k) * (a...inductive hypothesis implies that p | a_j for some j = 1,2,...,k. I hope that helps...

3 Answers · Science & Mathematics · 08/09/2009

9. ### Series/sequence question?

∑(n on top, i=1 bottom) a_i = a_1 + a_2 + ... + a_n but ∑(n top, i=1 bottom) a_ j = a_ j + a_ j + ... + a_ j = n * a_ j, since j is different from the index variable i. I hope that helps!

1 Answers · Science & Mathematics · 26/07/2009

10. ### Can you solve for me a_n= n^sin(n) using any test and if it converge, diverge, or neither?

...n) has a subsequence (n_j) such that sin(n_j) → -1, which implies a_n_j = n_j^sin(n_j) → 0. We see a_n has a subsequence that goes...

1 Answers · Science & Mathematics · 02/10/2008