dani8264 dani8264
  • 26-03-2021
  • Mathematics
contestada

Find the numerical answer to the summation given below.
75
Σ(6η + 10)
n=0

Respuesta :

kuellar
kuellar kuellar
  • 26-03-2021

Answer:

[tex]17860[/tex]

Step-by-step explanation:

To answer this, let's recall a few properties of summations:

[tex]\sum_{i=0}^{n}(a_i+b_i)=\sum_{i=0}^{n}a_i+\sum_{i=0}^{n}b_i\\\\ \sum_{i=0}^{n}(c*a_i)=c*\sum_{i=0}^{n}(a_i)\\\\ \sum_{i=0}^{n}(c)=(n+1)*c[/tex]

With these in mind, we can rewrite the given summation as follows:

[tex]\sum_{n=0}^{75}(6n+10)=\sum_{n=0}^{75}6n+\sum_{n=0}^{75}10=6*\sum_{n=0}^{75}n+76*10\\\\ =6*\frac{75*76}{2} +760=3*75*76+760=17860[/tex]

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