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How do you use sigma notation to write the sum for #1/(13)+1/(24)+1/(35)+...+1/(1012)#?

Answer 1

William Abdalla

#sum_(n=1)^12 1/(n(n+2))#

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Answer 2

Emma Aldridge

I give the sum here. #1/2(1+1/2 -1/11-1/12)=175/264#

The #sum# notation has already appeared, in the other answer.

As a matter of interest, I perform summation.

#1/(n(n+2))=1/2(1/n-1/(n+2))#.

So, the sum is

#1/2(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+...+1/9-1/11+1/10-1/12)#

#=1/2(1+1/2 -1/11-1/12)=175/264#

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Answer 3

Elijah Abram

To express the given sum using sigma notation, you can write:

∑(from k=1 to 10) 1 / (k * (k + 2))

This signifies the sum of the expression 1 / (k * (k + 2)) as k ranges from 1 to 10.

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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.

How do you use sigma notation to write the sum for #1/(1*3)+1/(2*4)+1/(3*5)+...+1/(10*12)#?

How do you use sigma notation to write the sum for #1/(13)+1/(24)+1/(35)+...+1/(1012)#?