1) There is an infinite staircase. Find the total volume of the staircase, given that the largest cube has a side of length 1 and each successive cube has a side whose length is half that of the preceding cube.

2) Show that for all real values of x

sinx-(1/2sin^(2)x)+(1/4sin^(3)x)-(1/8sin^(4)x)+...=(2sinx)/(2+sinx)