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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 ) =Σ a [ 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. ### 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

9. ### 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 · 07/09/2009

10. ### 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