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In Problems 61–70, express each sum using summation notation.

1+3+5+7+....+212-1

Short Answer

Expert verified

The required summation notation is 1+3+5+7+....+212-1=∑k=1n2k-1.

Step by step solution

01

Step 1. Write the given information.

The given sum is:

1+3+5+7+....+212-1
02

Step 2. Write the sum using summation notation.

Write each term in the same format:

1+3+5+7+....+212-1=21-1+22-1+23-1+.....+212-1=∑k=1n2k-1

As we can see that the sum21-1+22-1+23-1+.....+212-1 has 12 terms, each term represents the form 2k-1, and starts at k=1and ends at k=12.

Therefore,role="math" localid="1646761047379" 1+3+5+7+....+212-1=∑k=1n2k-1

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