How do you find the partial sum of #Sigma (250-8/3i)# from i=1 to 60?

Answer 1

The answer is 10120 (see below).

First, the commutative and distributive properties allow us to write:

#sum_{i=1}^{60}(250-8/3 i)=sum_{i=1}^{60}250-8/3 sum_{i=1}^{60}i#.

Now #sum_{i=1}^{60}250# is just 250 added to itself 60 times. Therefore #sum_{i=1}^{60}250=60*250=15000#.

Next, we can use the well-known formula for the sum of the first #n# integers (see https://tutor.hix.ai), which is #sum_{i=1}^{n}i=1+2+3+cdots+n=(n(n+1))/2#, to say

#sum_{i=1}^{60}i=(60*61)/2=30*61=1830#.

Hence, the answer is

#sum_{i=1}^{60}250-8/3 sum_{i=1}^{60}i#

#=15000-8/3 * 1830=15000-4880=10120#.

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Answer 2

Charles Arocha

#10120#

#sum_{i=1}^60 (250-8/3*i)=250*60-8/3*(60*61)/2=10120#

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Answer 3

Cameron Alexander

To find the partial sum of the series ( \sum_{i=1}^{60} (250 - \frac{8}{3i}) ), you need to substitute each value of ( i ) from 1 to 60 into the expression and then sum up the resulting terms.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.