SOLUTION: Prove using mathematical induction that for all n ≥ 1,
1 + 4 + 7 + · · · + (3n − 2) = n(3n − 1)
/2
Algebra.Com
Question 1189130: Prove using mathematical induction that for all n ≥ 1,
1 + 4 + 7 + · · · + (3n − 2) = n(3n − 1)
/2
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!
(1) Show that the formula is true for n=1
For n=1, the formula says
TRUE
(2) Show that, if the formula is true for some n, it is also true for n+1
We assume, as the formula says, that 1+4+7+...+(3n-2) is equal to and add the next term (, or ) and show that the resulting expression is equal to
=
=
=
The proof by induction is complete.
RELATED QUESTIONS
prove using mathematical induction:
1. 1^4 + 2^4 + 3^4 + ... + n^4 =... (answered by math_helper,robertb)
Use mathematical induction to prove the statement is true for all positive integers n, or (answered by Edwin McCravy)
Mathematical induction
How can we prove that :
(1 + 1 / 3) (1 + 5 / 4)(1 + 7 /... (answered by ikleyn)
Please help with this questions, prove by induction that the formulas positive integral... (answered by ikleyn)
Please help me solve and explain how to solve this mathematical induction:
Use... (answered by Edwin McCravy)
Induction Sum:
Prove using mathematical induction that:
1/1*2*3 + 1/2*3*4 + 1/3*4*5... (answered by robertb)
Pls help
USE MATHEMATICAL INDUCTION TO PROVE THAT
(n+1)^n < 2n^2 for all natural... (answered by ikleyn)
Use mathematical induction to prove the statement is true for all positive integers n.... (answered by ikleyn)
Use mathematical induction to prove the statement is true for all positive integers n.... (answered by math_helper)