7 . Suppose in Fig. 6 we begin with a square with sides of length 1 (area = 1) and construct another square inside by connecting the midpoints of the sides. Then the new square has area 1/2. If we continue the process of constructing each new square by connecting the midpoints of the sides of the previous square forever, we get an infinite sequence of squares each of which has 1/2 half the area of the previous square. Find the total area of all of the squares. Fig. 6 8. Find all values of x for which the geometric series converges and find its sum. * = 0 9. Calculate the value of the partial sum for n = 4 and n = 5 and find the limit of S, as n approaches infinity. 10. Show that the function determined by the terms of the given series satisfies the hypotheses of the Integral Test, and then use the Integral Test to determine whether the series converges or diverges. K2 sin k=1