Show that two sums are equal Show that
$\sum_{k=0}^4\left(1+x\right)^k$ = 
$\sum_{k=1}^5 \left(5 \choose k\right)x^{k-1}$
I assume that this has something to do with the binomial theorem and a proof of that. But I can't take the first steps...

The LHS is  a finite Geometric Series with the first term$=1,$ common ratio $=(1+x)$ and the number of terms $=5$
So, the sum is $$1\cdot\frac{(1+x)^5-1}{1+x-1}$$
Please expand using Binomial Expansion and cancel out $x$  to find it to be same as the RHS 
