(a) Write the sum 1 −
1
5
+
1
25
−
1
125
+
1
625
−
1
3125
+
1
15625
−
1
78125
+
1
390625
in summation notation over the range of summation the integer interval [2..10]. That
is, find an expression ak so that
X
10
k=2
ak
is equal to the given sum.
(b) Using your expression from part (a), consider the summation obtained by taking
the absolute value of each term:
X
10
k=2
|ak|
Express this summation as the summation of a finite difference.
Hint: Use one of the 3 examples we discussed in class.
(c) Shift the index in your summation from part (b) so that the summation starts at
k = 0 and determine the value of the summation without the use of a calculator!
That is, use the formula for telescoping summation, linearity of summation and a formula we discussed in class

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?