Question
Download Solution PDFFind the weighted arithmetic mean of the first 'n' natural numbers, the weights being the corresponding numbers.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept used:
1. Sum of the squares of first n natural numbers =
2. Sum of n natural numbers =
Calculation:
First n natural numbers = 1, 2, 3, ...., n
Their corresponding weights respectively = 1, 2, 3, ...., n
Now, the weighted arithmetic mean of the first 'n' natural numbers
⇒
⇒
⇒
⇒
∴ The weighted arithmetic mean of the first 'n' natural numbers is
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