Homework Statement
14
Ʃ 2(4/3)^n
n=1
Homework Equations
Sn=a(1-r^n)/(1-r)
The Attempt at a Solution
2(1-[4^14]/[3^14])/(-1/3)=330.74
However, the answer sheet gives ~441 as the answer, and I confirmed it by doing it by hand. Why is the equation not working? What's wrong?
Homework Statement
Two converging lenses of focal length=27cm are placed 16.5cm apart. If an object is placed 35cm in front of the first lens, where will the final image be produced? What will be the total magnification?
Homework Equations
1/f=1/di+1/do
do2=D-di1
M=-di/do
The...
Homework Statement
Prove that 3^n >= 2n+1 for all natural numbers.
Homework Equations
3^n >= 2n+1 [is bigger or equal to]
The Attempt at a Solution
3*1>=2+1
True for n=1
Assumption: 3^k>=2k+1
3^(k+1)>=2k+3
3^k*3>=2k+3
(2k+1)*3>=2k+3 <---can I just substitute 2k+1...