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Chapter 4: Q. 18 (page 403)

Fill in the blanks to complete each sum formula:

鈭�k=1nk=

Short Answer

Expert verified

The complete sum formula is鈭�k=1nk=n(n+1)2.

Step by step solution

01

Step 1. Given information.

Given incomplete sum formula is following.

鈭�k=1nk=

02

Step 2. proof

Write the expanded form of sigma notation.

鈭�k=1nk=1+2+3+鈰�(n-1)+n

The sum of the first and the last term is 1+n.

Similarly, the sum of the second and second last terms will be 2+(n-1)=n+1

The number of pairs whose sum is 1+nwill ben2.

So the sum of all pairs will ben2(n+1)=n(n+1)2

the sum of all pairs is equal to sigma notation.

so鈭�k=1nk=n(n+1)2

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