Base S(1)=1, so T(1)=S(1)
for some n, T(n)=S(n), then:
T(n+1) = 2T(n)+2 = 2(3×2^(n-1) -2) +2 = 3 × 2^n-4+2 = 3×2^n-2 = S(n+1)
Proof that T(n)=S(n) then T(n+1)=S(n+1), and as we have T(1)=S(1) i have proven by induction that T(n)=S(n) for any n in the positive integers
sorry its T2=1 / 2 = 1
the confusing part is why Sn is related to Tn , I am just going to base it on Tn.
The statement n > 1 is true
and by the replys i seem to have gone very wrong somewhere?
Hi all, I've been struggling with a large piece of coursework. been quite stressed latley and now I am struggling while aproaching my deadline. i need help answering this question.
Use mathematical induction to show that
S(n) = 3 × 2 n-1 -2
is the solution for the recurrence relation:
T(n)...
Im about to hand coursework in. Its the youngs modulus of copper wire
We added 100g weights and measured the extension using a traveling microscope.
for example at 0.900kg the wire extended by 6.36cm
my calculations are
Diameter = d 2.7x10-5 m
Cross section area A = Pi x d...
Basicly my stress and strain are
A = 5.73 x 10-3
L = 1.788m
F = 8.829 kg m s-1
e = 6.36cm or 6.36x10-1m
youngs modulus is 6.02x10(10) Pa
ive to find the % uncertainty in the Young Modulus value
Ive to work out the uncertainties for youngs modulus.
would i take all 4 measurements and mutliply then divide by 4 ?
would 1.788m have an uncertain if +/- 0.01 ?
how would i get the uncertainties from 5.73x10-3
im very confused and my tutor isn't helpful at all.
Hi there - My mistake was the diameter - it should have been calculated as 0.000573mm or 5.73x10-3
so the result in getting now is 6.03 x 10(10) Pa as the youngs modulus.
Im also working out the percentage error;
ive worked out the length as 1.788m +/- 0.01m so 0.01/1.788 x 100 = +/- 0.56%...