(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