Find the sum of the first 32 terms of the following series: 1.2 + 2.3 + 3.4 + 4.5 + ……
Question
Find the sum of the first 32 terms of the following series:
1.2 + 2.3 + 3.4 + 4.5 + ……
Solution
This is an arithmetic series where each term is the product of a natural number and its successor in decimal form.
The nth term of the series can be represented as n*(n+0.1).
The sum of the first N terms of an arithmetic series can be found using the formula:
S = n/2 * (a + l)
where: S is the sum of the first n terms, n is the number of terms, a is the first term, and l is the last term.
In this case, the first term a = 11.1 = 1.1 and the last term l = 3232.1 = 1024.
So, the sum of the first 32 terms is:
S = 32/2 * (1.1 + 1024) = 16 * 1025.1 = 16401.6
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