Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Proof by induction FP1 June 2014 (R)

Question 9 on June 2014 Regional.
I got to the point where i have (K)(2^K) + (K+2)(2^K)
And i'm unsure how to rearrange this to get (K+1)(2^K+1)
Thanks for the help!

Original post by Tom22561

Question 9 on June 2014 Regional.
I got to the point where i have (K)(2^K) + (K+2)(2^K)
And i'm unsure how to rearrange this to get (K+1)(2^K+1)
Thanks for the help!

k2^k +k 2^k + 2\cdot 2^k = 2^k(k + k+ 2)= (2k+2)2^{k} = 2(k+1)2^{k} = (k+1)2^{k+1}

.

OP

Original post by Zacken

k2^k +k 2^k + 2\cdot 2^k = 2^k(k + k+ 2)= (2k+2)2^{k} = 2(k+1)2^{k} = (k+1)2^{k+1}

.

That explains it thanks

Original post by Tom22561

That explains it thanks

No problem.

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