Maths induction (really need help!!!) (1 Viewer)

[plshelp]

Ok i dont really get this topic so i'm asking a lot of questions

Anyway the question is:

Given that Tn = 2*(Tn-1) + 1 and T1 = 5, prove that Tn = 6*2^(n-1) - 1

i got stuck halfway so maybe i'm not doing this right...so please help!! thanx

 

[timinator1993]

ok its like 6:30 am so kinda groggy.... but maby as 2 things are equal to Tn, set those equal to each other, and then just do the normal proving steps, where you change one of the sides until it equals the other? if that makes any sense at all

 

[ar7]

ok its like 6:30 am so kinda groggy.... but maby as 2 things are equal to Tn, set those equal to each other, and then just do the normal proving steps, where you change one of the sides until it equals the other? if that makes any sense at all

hahahahahaha lol

mate it aint simultaneous equations.

step 1. confirm T1 = 5
step 2. let n=k
step 3. form an equation for k+1 (so wereva k was, u use k + 1)
step 4. use the equation on the right side (Sk) and the one on the left (Tk)
step 5. add them (Sk + Tk = Sk+1) as essentially, you are proving they equal the equation you formed wen u subsituted in k+1.

therefore if true for n=1, and n=2 (n+1), it is true for all n.

 

[hscishard]

The k+1 is tricky. Not sure how to do it but I got the 6*2^(n-1) part. This is the difference in t1,t2,t3...