How to get this budget constraint? I have an Euler equation $ (\frac{ c_ {t+1} }{c_t})^\sigma = \beta (1+r)$,where $c_t$ is the t period consumption,r is interest rate and $\beta$ is discount rate, and a budget constraint $\sum _{t=0}^\infty \frac{c_t}{(1+r)^t}=\sum _{t=0}^\infty \frac{y_t}{(1+r)^t}$, where $y_t$ is income.

My question is how to substitute Euler equation into budget constraint to get the following equation?

$c_t\sum_{j=0}^\infty\frac{[\beta(1+r)]^\frac{j}{\sigma}}{(1+r)^j}=\sum _{t=0}^\infty \frac{y_t}{(1+r)^t}$
The hint is to use the recursive Euler equation to express all future consumptions $c_{t+j}$ as a function of current consumption $c_t$, and to play with the indexes in the sum of the left.