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Chapter 7: Q. 5 (page 614)

What is the relationship between ∑k=1∞ak,∑k=10∞ak? If you knew that ∑k=10∞akconverged to42, what other information would you need to know to find the sum of∑k=1∞ak?

Short Answer

Expert verified

The required relationship is ∑k=1∞ak=∑k=19ak+∑k=10∞ak.

To find the sum of ∑k=10∞ak, first it is required to know∑k=19ak.

Step by step solution

01

Step 1. Given information.

Consider the given question,

The series ∑k=1∞ak,∑k=10∞akand the series∑k=10∞akis converging to42.

02

Step 2. 

The series ∑k=1∞akis written as,

∑k=1∞ak=∑k=19ak+∑k=10∞ak......(i)

To find the sum of ∑k=1∞ak, the sum of the series ∑k=1∞akis needed because from equation (i),

The sum of ∑k=10∞akis known and only value needed is ∑k=19ak.

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