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anonymous
 one year ago
For the given statement Pn, write the statements P1, Pk, and Pk+1.
(2 points)
2 + 4 + 6 + . . . + 2n = n(n+1)
Would the answer just be: (k+1)(k+2) ?
anonymous
 one year ago
For the given statement Pn, write the statements P1, Pk, and Pk+1. (2 points) 2 + 4 + 6 + . . . + 2n = n(n+1) Would the answer just be: (k+1)(k+2) ?

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campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1well that is the sum of k + 1 terms....

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1the left side contains the terms including the general term 2n the right side contains the sum of the terms n(n + 1) so n = 1 term 1 = 2 the sum of 1 term 1(1 + 1) 2 the kth term 2k the sum of k terms is k(k + 1) the k + 1 term 2(k + 1) the sum is (k +1)(k + 2) this seems a lot like mathematical induction.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, it is. But what should the final answer even look like? I'm confused by the problem.

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1ok... so its true for n = 1 assume that for n = k the sum is k(k +1) now for the k + 1 term term k+ 1 = 2(k + 1) or 2k+ 2 if you add this to the sum of k terms you should get (k + 1)(k + 2) so sum of term k + 1 and the sum of k terms 2(k + 1) + k(k + 1) both terms have a common factor of (k + 1) so it can be written as (k + 1)(2 + k) or (k + 1)(k + 2) (1) now using the sum n(n + 1) for k + 1 terms it becomes (k + 1)(k + 1+1) or (k + 1)(k+2) so you have shown that the sum of k terms and the k + 1 term is equal to the sum of k +1 terms.. hope that makes sense

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So what I wrote is correct then?
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