Question

Arrange the summation expressions in increasing order of their values.

Answer 1

∑ 4 * 5^(i-1) = 4 + 20 + 100 + 500 = 624

∑ 3 * 4^(i-1) = 3 + 12 + 48 + 192 + 768 = 1,023

∑ 5* 6^(i-1) = 5 + 30 = 35

∑ 5^(i-1) = 1 + 5 + 25 + 125 = 156

Answer:

∑ (i=1, 2) 5 * 6^(i-1) < ∑ (i=1, 4) 5^(i-1) < ∑ (i=1, 4) 4 * 5^(i-1) <

< ∑ (i=1, 5) 3 * 4^(i-1)

Answer 2

We'll solve for each one of them:


`\sum_(i=1)^(4)4(5)^(i-1) = (4(5)^(1-1)) + (4(5)^(2-1)) + (4(5)^(3-1)) + (4(5)^(4-1))`

`=4+20+100+500 = 624`


`\sum_(i=1)^(5)3(4)^(i-1) = (3(4)^(1-1)) + (3(4)^(2-1)) + (3(4)^(3-1)) + (3(4)^(4-1)) + (3(4)^(5-1))`

`=3+12+48+192+768=1023`


`\sum_(i=1)^(2)5(6)^(i-1) = (5(6)^(1-1)) + (5(6)^(2-1))`

`=5+30=35`


`\sum_(i=1)^(4)5^(i-1) = (5^(1-1))+(5^(2-1))+(5^(3-1))+(5^(4-1))`

`=1 + 5+ 25+125 = 156`

So, our totals are: 624, 1023, 35, and 156. So clearly, 1023 > 624 > 156 > 35. W can write it as (your answer):


`\sum_(i=1)^(2)5(6)^(i-1) <\sum_(i=1)^(4)5^(i-1) <\sum_(i=1)^(4)4(5)^(i-1) < \sum_(i=1)^(5)3(4)^(i-1)`

Hope this helps! If anything is confusing, you can always DM me.