Question

Write the following two sequences using summation notation:

Answer 1

Answer:

Step-by-step explanation:

Sequence 1:

This is a finite sequence ending with 40

5-10+15-20+...40

= 5(1-2+3-4+5-6+7-8) (by taking 5 as common factor)

This is an alternating series with even numbers in the series having negative sign

Hence can be written as

$\Sigma _{1} ^{8} 5[(-1)^{n-1} (n)$

This gives the I sequence in the summation notation.  Since there are only 8 terms n can take values as 1 to 8, with odd terms positive.

---------------------------------

Sequence 2:

This is the same as the previous sequence but with end point as infinite

This is an infinite series. Hence n can vary from 1 to infinity.

Thus sum would be

$\Sigma _{1} ^{\infty } 5[(-1)^{n-1} (n)$

(Note that only the ending number is difference for both.)