Sequences and Series Question (1 Viewer)

[phoenix159]

Find the sum of the first n terms of T_r = 2^r + 2r - 1 (its the sum of an arithmetic and geometric series)

I got n² - n/2 + 2ⁿ⁺¹ - 2

But the textbook says n² + 2ⁿ⁺¹ - 2

 

[bottleofyarn]

Find the sum of the first n terms of T_r = 2^r + 2r - 1 (its the sum of an arithmetic and geometric series)

I got n² - n/2 + 2ⁿ⁺¹ - 2

But the textbook says n² + 2ⁿ⁺¹ - 2

It looks like you've got the geometric sum down pat (2ⁿ⁺¹ - 2) So then it's just a matter of the arithmetic sum and -1s. My guess is that you missed the multiplication by 2 since
.
Stuff cancels out and it should give you the answer.

 

[phoenix159]

Thanks!