Mathematical induction help (1 Viewer)

[Hermes1]

prove for all positive integers n:

1 + 2+ 2^2 + 2^3 +.......+ 2^n = 2^n+1 -1

im not able to prove true for n = 1

 

[Bored Of Fail]

prove for all positive integers n:

1 + 2+ 2^2 + 2^3 +.......+ 2^n = 2^n+1 -1

im not able to prove true for n = 1

NOTE the LHS starts at n=0 ( ie 1 = 2^0 )

so that means that if you want to prove it true for n=1 you need to sum the first 2 terms of the LHS

that is 1 + 2 = 2^(1+1) - 1 which is true

your starting case should be n=0 , not n=1 ( well it doesnt have to be as it says "POSITIVE" integers n, but if you want to start n=1 you need to sum the first 2 terms of the LHS )

 

[Hermes1]

tnx. that was a really fast reply lol.