Answer:
1.one solution is the answer
Step-by-step explanation:
Let's focus on 0.7*0.8 for now.
Start by drawing a large square. Cut this figure into 10 rows and 10 columns. So this means you'll have 10*10 = 100 little squares.
Now highlight the first 7 rows. Shade in all 70 squares (7*10 = 70)
Starting on the left side, highlight the first 8 columns. You'll shade in 80 squares (8*10 = 80)
Use different colors for your highlighting or somehow indicate different shading styles. This way you can see the overlapping region. The overlapping region consists of 56 squares (7 rows, 8 columns ---> 7*8 = 56 little squares)
Each little square represents 0.01, so having 56 of them means we have 0.56
This shows that 0.7*0.8 = 0.56
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How is this different if we had 1.7*0.8? Well we can break 1.7 into 1+0.7 to have
1.7*0.8 = (1+0.7)*0.8
1.7*0.8 = (1)*0.8+(0.7)*0.8
1.7*0.8 = (1*0.8)+(0.7*0.8)
The portion (0.7*0.8) was done earlier. That result was 0.56. So we just need to compute (1*0.8), which is simply 0.8; recall that 1 times any number is that number itself.
Now simply add 0.8 to 0.56 to get 1.36
So, 1.7*0.8 = 1.36
600 + 300 + 150 + . . . is a geometric sequence with a = 600 and r = 1/2
Sn = a(1 - r^n)/(1 - r)
S5 = 600(1 - (1/2)^5)/(1 - 1/2) = 600(1 - 1/32)/(1/2) = 1,200(31/32) = 1,162.5
