anonymous
  • anonymous
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) ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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campbell_st
  • campbell_st
well that is the sum of k + 1 terms....
campbell_st
  • campbell_st
the 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
  • anonymous
Yes, it is. But what should the final answer even look like? I'm confused by the problem.

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anonymous
  • anonymous
@campbell_st
campbell_st
  • campbell_st
ok... 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
  • anonymous
So what I wrote is correct then?
anonymous
  • anonymous
@campbell_st
campbell_st
  • campbell_st
yes...
anonymous
  • anonymous
Ok thanks so much!

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