help with maths in focus (1 Viewer)

[fredinho]

Question 15
Chapter 8.2

Find the sum of the first 10 terms of the series 3+7+13+...+[2^n+(2n-1)]

 

[Fortify]

Split [2^n + (2n-1)]; so:

A = 2^n and b = (2n-1)

So A = 2^1 + 2 ^ 2 + 2 ^ 3 + ... + 2^10
A = 2 (2^10 - 1) / (2 - 1) = 2046

Now:

B = (2(1)-1) + (2(2)-1) + ... + (2(10)-1)
B = 1 + 3 + ... + 19
B = 10/2 (1+19)
B = 100

Therefore:

S10 = A + B = 2146.