Respuesta :

Answer:

The given sums 11+17+23+29+35+41  can be written as in sigma notation is  [tex]\sum\limits_{i=1}^{6}5+6i[/tex]

Therefore 11+17+23+29+35+41=[tex]\sum\limits_{i=1}^{6}5+6i[/tex]

Step-by-step explanation:

Given series is 11+17+23+29+35+41

To find the given sum expressed in sigma notation :

11+17+23+29+35+41  can be written as the given sums in sigma notation is  [tex]\sum\limits_{i=1}^{6}5+6i[/tex]

That is

11+17+23+29+35+41=[tex]\sum\limits_{i=1}^{6}5+6i[/tex]

Now expand the sums and to verify that whether the summation is true or not :

[tex]\sum\limits_{i=1}^{6}5+6i=(5+6(1))+(5+6(2))+(5+6(3))+(5+6(4))+(5+6(5))+(5+6(6))[/tex]

[tex]=(5+6)+(5+12)+(5+18)+(5+24)+(5+30)+(5+36)[/tex]

[tex]=11+17+23+29+35+41[/tex]

Therefore 11+17+23+29+35+41=[tex]\sum\limits_{i=1}^{6}5+6i[/tex]

The sum can be expressed as [tex]\sum_{(i=1)}^6 = 5+6i[/tex].

Given to us,

  • 11 + 17 + 23 + 29 + 35 + 41

As we can see in the following series,

Every number in the series can be expressed in the form of (5+6i) where i is the position of the series,

  • 11 = 5 + 6(1),
  • 17 = 5 + 6(2),
  • 23 = 5 + 6(3),
  • 29 = 5 + 6(4),
  • 35 = 5 + 6(5),
  • 41 = 5 + 6(6),

Verification

The sum can be verified by expanding the sum from i=1 to6.

[tex]\sum_{(i=1)}^6 = 5+6i\\\sum_{(i=1)}^6 = [5 + 6(1)]+[5 + 6(2)]+[5 + 6(3)]+[5 + 6(4)]+[5+ 6(5)]+[5 + 6(6)]\\\sum_{(i=1)}^6 = 11 + 17 + 23 + 29 + 35 + 41\\\sum_{(i=1)}^6 = 156[/tex]

therefore, the sum can be expressed as,

[tex]\sum_{(i=1)}^6 = 5+6i[/tex].

Learn more about sigma notation:

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