Chapter 4: Q. 45 (page 326)

Find the sum or quantity without completely expanding or calculating any sums.
Given $\sum_{k = 1}^{4} a_{k} = 7$ and $, \sum_{k = 0}^{4} b_{k} = 10$ , $a_{0} = 2$ . Find the value of $\sum_{k = 0}^{4} (2 a_{k} + 3 b_{k})$ .

Short Answer

Expert verified

The sum is $48$ .

Step by step solution

Step 1. Given information

$\sum_{k = 1}^{4} a_{k} = 7 \sum_{k = 0}^{4} b_{k} = 10 a_{0} = 2$

Step 2. Find the sum:

$\sum_{k = 0}^{4} (2 a_{k} + 3 b_{k}) = \sum_{k = 0}^{4} 2 a_{k} + \sum_{k = 0}^{4} 3 b_{k} = 2 a_{0} + \sum_{k = 1}^{4} 2 a_{k} + \sum_{k = 0}^{4} 3 b_{k} = 2 a_{0} + 2 \sum_{k = 1}^{4} a_{k} + 3 \sum_{k = 0}^{4} b_{k} = 2 \times 2 + 2 \times 7 + 3 \times 10 = 4 + 14 + 30 = 48$

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Find the sum or quantity without completely expanding or calculating any sums.
Given $\sum_{k = 1}^{4} a_{k} = 7$ and $, \sum_{k = 0}^{4} b_{k} = 10$ , $a_{0} = 2$ . Find the value of $\sum_{k = 0}^{4} (2 a_{k} + 3 b_{k})$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the sum:

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Find the sum or quantity without completely expanding or calculating any sums.Given ∑k=14ak=7and,∑k=04bk=10,a0=2. Find the value of∑k=042ak+3bk.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the sum:

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Most popular questions from this chapter

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Decision Maths

Mechanics Maths

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Theoretical and Mathematical Physics

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Find the sum or quantity without completely expanding or calculating any sums.
Given $\sum_{k = 1}^{4} a_{k} = 7$ and $, \sum_{k = 0}^{4} b_{k} = 10$ , $a_{0} = 2$ . Find the value of $\sum_{k = 0}^{4} (2 a_{k} + 3 b_{k})$ .