How Gauss Did It 1 + 2 + 3 + . . . + n =

2. Triangular Numbers Tn = 1 + 2 + 3 + . . . + n =

3. Sum of Squares (understand how to find the sum using the proofs in both parts)

12 + 22 + 32 + . . . + n2 =

7. Exponential Sums (Do parts a and b only)

a) 2 0 + 21 + 22 + 23 + . . . + 2n–1 =

b) a 0 + a 1 + a 2 + a 3 + . . . + a n–1 =

1; 35 is the ratio

step-by-step explanation:

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

i think u have 12 apples sorry again i don't really know if it correct i'm just tryna hrlp people out.

0.038

step-by-step explanation: