Proofs Induction Question (1 Viewer)

hmim · Mar 30, 2023

Hey can someone show me how to do this question please, particularly the proving n = k+1 part

Drongoski · Mar 30, 2023

For (a) hypothesis step:

$\sum _{r=1} ^k (r+1)\times 2^r = k\times2^{k+1} \\ \\ \therefore \sum _{r=1}^{k+1} = k\times2^{k+1} + (k+1 + 1)\times 2^{k+1} = 2(k+1) \times 2^{k+1} = (k+1)\times 2^{k+1 +1}$

So if true for n=k, true also for n=k+1 . . . blah blah blah

Proofs Induction Question (1 Viewer)

hmim

Member

Drongoski

Well-Known Member

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