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Chapter 4: Q. 13 (page 403)

The algebra of sums: Fill in the blanks to complete the sum rules that follow. You may assume that akand bkare functions defined for nonnegative integers kand that cis any real number.

鈭�k=1ncak=______

Short Answer

Expert verified

鈭�k=1ncak=c鈭�k=1nak.

Step by step solution

01

Step 1. Given information

鈭�k=1ncak.

02

Step 2. First translate the sigma notation to its expanded form and then apply the distributive property:

鈭�k=1ncak=ca1+ca2+ca3+鈰�+can-1+can

Now factor out the common terms.

ca1+ca2+ca3+鈰�+can-1+can=ca1+a2+a3+鈰�+an-1+an.

Now write in sigma notation.

role="math" localid="1648821440325" ca1+a2+a3+鈰�+an-1+an=c鈭�k=1nak.

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