Question

HELP DUE SOON SOON SOON SOOON

Answer 1

second choice

Explanation:

The given sums ∑ have j = 1, j = 2, j = 3, j = 4, j = 5

Consider first j = 1 and substitute in the answers to see if we get the first term of the series -3

`-3((1)/(3) )^(1-1) = -3((1)/(3) )^(0)= -3*1= -3` ✅

2·1 - 5 = 2-5 = -3 ✅

3·1 - 6 = 3-6 = -3 ✅

`5^(1-1) = 5^(0) = 1` ❌

We see that last choice gives us as first term to be 1 not -3 so eliminate that possibility.

Consider now j = 2 and substitute in the answers to see if we get the second term of the series -1

`-3((1)/(3) )^(2-1) = -3((1)/(3) )^(1)= (-3)/(3) = -1` ✅

2·2 - 5 = 4-5 = -1 ✅

3·2 - 6 = 6-6 = 0 ❌

We see that third choice gives us as second term to be 0 not -1 so eliminate that possibility.

Consider now j = 3 and substitute in the answers to see if we get the third term of the series 1

`-3((1)/(3) )^(3-1) = -3((1)/(3) )^(2)= (-3)/(9) = (-1)/(3)` ❌

2·3 - 5 = 6-5 = 1 ✅

We see that first choice gives us as third term to be -1/3 not 1 so eliminate that possibility.

Now we are left with the second choice as the only possibility.