• Best of luck to the class of 2024 for their HSC exams. You got this!
    Let us know your thoughts on the HSC exams here
  • YOU can help the next generation of students in the community!
    Share your trial papers and notes on our Notes & Resources page
MedVision ad

help with maths in focus (1 Viewer)

fredinho

New Member
Joined
Apr 17, 2009
Messages
17
Gender
Male
HSC
2009
Question 15
Chapter 8.2

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

Fortify

♪웨딩드레스
Joined
Mar 20, 2007
Messages
1,281
Gender
Male
HSC
2009
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.
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top