Question

Compute each sum below. If applicable, write your answer as a fraction.

5+5(-2)+5+(-2)^2+...+5(-2)^7=

9
∑ (1/4i)=
i=1

Answer 1

First equation is -425

Second equation is 11.25

Explanation:

First equation we can write as

`\sum_(i=0)^7 5 * (-2)^i`

computing

When i=0 ->
`5 * (-2)^0 =5`

When i=1 ->
`5 * (-2)^1 = -10`

...

When i=7 ->
`5 * (-2)^7 = --640`

then replacing each term we have

`5  + (-10) + ( 20) + ( -40) +  (80) +( -160) +   320 + (-640) = -425`

For the second equation we'll have 9 terms, solving in a similar fashion

When i=1 ->
`(1)/(4)1=0.25`

When i=2 ->
`(1)/(4)2=0.50`

When i=3 ->
`(1)/(4)3=0.75`

...

When i=9 ->
`(1)/(4)9=2.25`

So we have 0.25 + 0.50 + 0.75 + 1.00 + 1.25 + 1.50+ 1.75 +2.00 +2.25