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Aleks [24]
3 years ago
12

Find the sum of the summation of 3 i minus 15, from i equals 2 to 7.

Mathematics
2 answers:
Mrac [35]3 years ago
3 0
The summation symbol means we use the variable i in the equation from the given range. In this case, we are given with the equation 3 i - 15 and i ranges from 2 to 7. The summation using simply the calculator is equal to -9. The answer to this problem is -9.
Shkiper50 [21]3 years ago
3 0

Answer:

\sum _{i=2}^73i-15=-9

Step-by-step explanation:

Given : \sum _{i=2}^73i-15

We have to evaluate the given summation.

Consider \sum _{i=2}^73i-15

using, we have,

\sum _{k=m}^n\:=\:\sum _{k=1}^n\:-\:\sum _{k=1}^{m-1}

=\sum _{i=1}^73i-15-\sum _{i=1}^13i-15      ..............(1)

Consider, \sum _{i=1}^73i-15

Apply sum rule,

\quad \sum a_n+b_n=\sum a_n+\sum b_n , we have,

=\sum _{i=1}^73i-\sum _{i=1}^715

Now, first consider, \sum _{i=1}^73i

Apply constant multiplication rule,\quad \sum c\cdot a_n=c\cdot \sum a_n we have,

=3\cdot \sum \:_{i=1}^7i

=3\cdot \:28\\\\=84

Also, \sum _{i=1}^715=105

Thus, \sum _{i=1}^73i-15=84-105=-21

Similarly, \sum _{i=1}^13i-15=-12

Substitute in (1) , we have,

Thus, \sum _{i=2}^73i-15=-21-(-12)=-21+12=-9

Thus, \sum _{i=2}^73i-15=-9

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