Asked by Timofey
Use mathematical induction to prove that the statement holds for all positive integers. Also, label the basis, hypothesis, and induction step.
1 + 5 + 9 + … + (4n -3)= n(2n-1)
1 + 5 + 9 + … + (4n -3)= n(2n-1)
Answers
Answered by
Steve
for k=1: 1 = 1(2-1)
assume for k
for n=k+1,
1+5+...+(4k-3)+(4(k+1)-3) = k(2k-1) + (4(k+1)-3)
= k(2k-1) + (4k+1)
= 2k^2 - k + 4k + 1
= 2k^2 + 3k + 1
= (k+1)(2k+1)
= (k+1)(2(k+1)-1)
assume for k
for n=k+1,
1+5+...+(4k-3)+(4(k+1)-3) = k(2k-1) + (4(k+1)-3)
= k(2k-1) + (4k+1)
= 2k^2 - k + 4k + 1
= 2k^2 + 3k + 1
= (k+1)(2k+1)
= (k+1)(2(k+1)-1)
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.