For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is give by (see attachment). If T is the sum of the first 10 terms in the sequence, then T is
greater than 2
between 1 and 2
between 1/2 and 1
between 1/4 and 1/2
less than 1/4
Notice that the answer choices are RANGES.
We are not expected to calculate the exact sum.
Use a NUMBER LINE to determine the correct range.
Follow the arrows.
The first term is 1/2.
When we add in -1/4 -- the second term -- the sum decreases to 1/4.
When we add in +1/8 -- the third term -- the sum increases to 3/8.
By now, we can already see that the sum will converge to a value somewhere between 1/4 and 3/8.
The correct answer is
D.
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