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What is ∑n=124(2n−3) equal to?
24
∑ (2n−3)
n=1

What is ∑n=124(2n−3) equal to? 24 ∑ (2n−3) n=1-example-1

1 Answer

1 vote

Answer: 528

Explanation:

The expression ∑n=1^24 (2n−3) represents the sum of the expression (2n−3) as n takes on values from 1 to 24. To calculate this sum, you can use the formula for the sum of an arithmetic series:

∑n=1^24 (2n−3) = [n(n+1)/2] * (2n−3)

Now, plug in the values for n from 1 to 24 and calculate each term in the sum:

= [1(1+1)/2] * (2(1)−3) + [2(2+1)/2] * (2(2)−3) + ... + [24(24+1)/2] * (2(24)−3)

Now, compute each term:

= [1(2)/2] * (2−3) + [2(3)/2] * (4−3) + ... + [24(25)/2] * (48−3)

= (1) * (-1) + (3) * (1) + (6) * (3) + ... + (300) * (45)

Now, sum up all these individual terms:

= -1 + 3 + 18 + ... + 13500

To find this sum, you can use the formula for the sum of an arithmetic series:

Sum = (n/2) * [2a + (n-1)d]

In this case, a is the first term (-1), n is the number of terms (24), and d is the common difference (2).

Sum = (24/2) * [2(-1) + (24-1)(2)]

Now, calculate this sum:

Sum = 12 * [-2 + 46]

Sum = 12 * 44

Sum = 528

So, ∑n=1^24 (2n−3) is equal to 528.

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