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Chapter 4: Q. 59 (page 327)

Given a simple proof that $\sum_{k = 0}^{n} 3 a_{k} = 3 \sum_{k = 0}^{n} a_{k}$

Short Answer

Expert verified

We have proved $\sum_{k = 0}^{n} 3 a_{k} = 3 \sum_{k = 0}^{n} a_{k}$

Step by step solution

Given information

We are given a relation $\sum_{k = 0}^{n} 3 a_{k} = 3 \sum_{k = 0}^{n} a_{k}$ . We have to prove it

Proof

We have,

$\sum_{k = 0}^{n} 3 a_{k} = 3 a_{1} + 3 a_{2} + . . . . + 3 a_{n} = 3 (a_{1} + a_{2} + . . . . + a_{n}) = 3 \sum_{k = 0}^{n} a_{k} = R H S$

Hence proved

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Most popular questions from this chapter

Calculate the exact value of each definite integral in Exercises 47–52 by using properties of definite integrals and the formulas in Theorem 4.13.

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If $\int_{- 2}^{3} f (x) d x = 4, \int_{- 2}^{6} f (x) d x = 9, \int_{- 2}^{3} g (x) d x = 2$ and $\int_{3}^{6} g (x) d x = 3$ ,then find the values of each definite integral in Exercises $29 - 40$ . If there is not enough information, explain why.

$\int_{3}^{6} f (x) d x$ .

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Given a simple proof that∑k=0n3ak=3∑k=0nak

Short Answer

Step by step solution

Given information

Proof

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Most popular questions from this chapter

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Given a simple proof that $\sum_{k = 0}^{n} 3 a_{k} = 3 \sum_{k = 0}^{n} a_{k}$