A man is on block 2, find expected number of steps for him to reach block 1. 
There are infinite blocks placed along positive axis at integer points. A man is on position $2$. He moves back one step with probability $p$ and forward with probability $1-p$ where $p > 0.5$.
  Find expected number of steps for him to reach first block.

I denoted expected number of steps to reach block $1$ when on ith block as $E_i$
Then $E_1 = 0$ and we need to find $E_2$. Further there is a relation:
$$E_k = p(E_{k-1}+1)+(1-p)(E_{k+1}+1)$$
Now I dont have any ideas. 

If you take a step forward, notice how the situation is similar, if you now ask the expected number of steps to return to tile $2$. So it will also take $E_2$ steps on average to go back to tile $2$ when you're on tile $3$, and then again $E_2$ to go from $2$ to $1$.  So we can write
$$E_2 = p\times 1 + (1-p)\times(1+2E_2)$$
and solve
$$E_2 = \frac{1}{2p-1}$$
We need to know that the expectancies are finite (which is the case when $p>0.5$), for this to make sense. For more information see here.
