Hey guys,

ive got a question to solve:

It goes like this:

Using mathematical Induction, prove that

SUM(r=1->n) of (r+1)2^r-1 = n(2^n)

Now the basic step is easy so im not gonna bother typing it here now but later on:

I get that:

(Let P(k) be true so:)

Sum(r=1->k) of (r+1)2^r-1 = k(2^k)

Now prove that P(k+1) is true:

Sum(r=1->k+1) of (r+1)2^r-1 = (k+1)(2^(k+1))

The Lefthandside of the equation above says:

Sum(r=1->k+1) of (r+1)2^r-1

We can expand this to be

Sum(r=1->k) of (r+1)2^r-1 + ((k+1)+1)2^(k+1)-1

Using our assumption of the beginnig we can say now that:

k(2^k) + ((k+1)+1)2^(k+1)-1 must equal this if i havenīt done any mistakes: (k+1)(2^(k+1)), doesnīt it.

But somehow i canīt get that,

if some could just show me the last step then iīd be fine with that.

Hope i`ve expressed my self correctly in that question. (Couldnīt really get used to the commands quick menu; sorry)

Cheers guys