SOLUTION: Suppose in a proof of the summation formula 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1) by mathematical induction, you show the formula valid for n = 1 and assume that it is valid for n

Question 1035624: Suppose in a proof of the summation formula 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1) by mathematical induction, you show the formula valid for n = 1 and assume that it is valid for n = k. What is the next equation in the induction step of this proof?
1 + 5 + 9 + ... + (4k - 3) = k(2k - 1) + (4(k+1) - 3)
1 + 5 + 9 + ... + (4k - 3) + (4(k+1) - 3) = k(2k - 1) + (4(k+1) - 3)
1 + 5 + 9 + ... + (4k - 3) + (4(k+1) - 3) = k(2k - 1) + (k + 1)[2(k + 1) - 1]
1 + 5 + 9 + ... + (4k - 3) = k(2k - 1)
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
From the second line of the proof...
1 + 5 + 9 + ... + (4k - 3) + (4(k+1) - 3) = k(2k - 1) + (4(k+1) - 3)
=
RELATED QUESTIONS
Suppose in a proof of the summation formula 7 + 9 + 11 + ... + (2n + 5) = n(n + 6) by... (answered by robertb)

Suppose in a proof of the summation formula 7 + 9 + 11 + ... + (2n + 5) = n(n + 6) by... (answered by ikleyn)

Use mathematical induction to prove the following: For each natural number... (answered by Edwin McCravy,amalm06)

use mathematical induction to prove the summation formula: {{{sum((4i-1),1=1,n)}}} =... (answered by Edwin McCravy)

Let P(n) be the statement that 3^1 + 3^2 + � � � 3^n = 3/2(3^n-1) for the positive... (answered by ikleyn)

use mathematical induction to prove the summation of  i=1... (answered by KMST)

use the principals of mathematical induction to prove the following statement... (answered by greenestamps)

please help me with this use the method of mathematical induction to prove the following (answered by math-vortex)

Prove the following using mathematical induction. Be sure to show the anchor as well as... (answered by math_helper)