# Mathematical Induction

Use mathematical induction to prove that the following is true.

8+11+14...+(3n+5)=1/2n(3n+13), for all n in the set of natural numbers.

1. prove that P(1) is true:
8 = 1/2 1(3*1+13) = 16/2 = 8

Assuming P(k), see what P(k+1) means:

8+11+...+(3k+5)+(3(k+1)+5) = k/2 (3k+13) + (3(k+1)+5)
= k/2 (3k+13) + 3k+8
1/2 (3k^2+13k + 6k+16)
= 1/2 (3k^2+19k+16)
= 1/2 (k+1)(3k+16)
= 1/2 (k+1)(3(k+1)+13)
= P(k+1)

So, P(1) and P(k) ==> P(k+1)

posted by Steve

## Similar Questions

1. ### Mathematical induction. I'm stuck. So far I have..

For all integers n ≥ 1, prove the following statement using mathematical induction. 1+2^1 +2^2 +...+2^n = 2^(n+1) −1 Here's what I have so far 1. Prove the base step let n=1 2^1=2^(1+1)-1 False. Someone else suggested
2. ### precalculus

Find Pk + 1 if Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) 7 + 13 + 19 + …+[6(k - 1) + 1] + (6k + 1) + [6(k + 1) + 1] 8 + 14 + 20 + …+[7(k - 1) + 1] + (7k + 1) 7 + 13 + 19 + …+(6k + 1) 7 + 13 + 19 + ...+[6(k - 1) + 1] +
3. ### Mathematical Induction

I have been given that a1 = 1 and an+1 = 1/3*(an + 4). In order to prove that this sequence is monotonous, what is the second step of mathematical induction? If my explaining of the question is unclear, here is a picture of the
4. ### Math

Use mathematical induction to prove that 5^(n) - 1 is divisible by four for all natural numbers n. Hint: if a number is divisible by 4, then it has a factor of 4. also, -1 = -5 +4 This is a take home test so I don't want the
5. ### Math - Mathematical Induction

3. Prove by induction that∑_(r=1)^n▒〖r(r+4)=1/6 n(n+1)(2n+13)〗. 5. It is given that u_1=1 and u_(n+1)=3u_n+2n-2 where n is a positive integer. Prove, by induction, that u_n=3^n/2-n+1/2. 14. The rth term
6. ### Math..mathematical induction

Prove by mathematical induction that 1+3+5+7+....+(2n-1)=n²
7. ### Calculus

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)
8. ### pre-calc

Use mathematical induction to prove that the statement is true for every positive integer n. Show your work. 2 is a factor of n2 -n+2
9. ### pre calc

Use mathematical induction to prove that the statement is true for every positive integer n. Show your work. 2 is a factor of n2 - n + 2
10. ### pre calc

Use mathematical induction to prove that the statement is true for every positive integer n. Show your work. 2 is a factor of n2 - n + 2

More Similar Questions