Find the sum of the series
15
1
(2 1)
n
n

  . Show your work.

225

Step-by-step explanation:

Using the basic components of summation ∑

∑n = n(n + 1) and ∑1 = n

Thus

∑ (2n - 1) ← for n = 1 to 15

= ∑2n - ∑1

= 2∑n - ∑1

= 2 ( n(n + 1)) - n

= n(n + 1) - n ← Evaluate for n = 15 ( the upper value )

= 15 × 16 - 15

= 240 - 15

= 225

529 and 531

step-by-step explanation:

probably .5

i can on others if necessary.