the formula 1/2(n^2+n) finds the sum of the first n positive integers. find the sum of the first 5 integers, then use the formula to prove you got the same answer. finally use the formula to find the sum f the first 14 integers. answer asap for brainliest worth 30 points.

Induction is done by demonstrating that if the condition is true for some n then it must also be true for n+1. If you then show that the condition is true for n=0 then it must be true for all n>0. For this problem:

Step 1: n=1

The sum of the first 1 odd numbers is 1. 12=1. Therefore the condition holds for n=1.

Step 2: induction

If the sum of the first n odd numbers is n2 then the sum of the first n+1 integers is n2+(2n+1)=(n+1)(n+1)=(n+1)2

So the condition is also true for n+1.

Step 3: conclusion

Since the we have shown that the condition is true for n=1 and we have shown that if it is true for n then it is also true for n+1 then it follows by induction that it is true for all n≥1.

Step-by-step explanation:

sorry if wrong

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1