Find the sum of the series . Show your work

We can first plug in the values of n, to find a pattern.

 

When n = 1, 2*1 - 1 = 1

 

When n = 2, 2*2 - 1 = 3

 

When n = 3, 2*3 - 1 = 5

 

...

 

When n = 15, 2*15 - 1 = 29

 

We see the pattern, 1, 3, 5, 7, ..., 29.

 

We find the sum 1 + 3 + 5 + ... + 29.

 

1 + 3 + ... n + 1 = n ^ 2

 

(29 - 1)^2 = 784

 

That is your final answer. 

 

I hope this helped,

 

Gavin.

1, 3, 5, 7........29.

[29 - 1] / 2 + 1 = 15 number of terms

15^2 =225 Sum of the 15 terms, which is the same as:

∑[2n -  1], n=1 to 15 = 225