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waheguru
I don't understand this question The sum of the first "n" natural numbers is a quadratic relation. Determine that relation and verify it for the first 6 natural numbers
We would be talking about the sum of this arithmetic series: 1,2,3,4,5,...n-1, n
Can you show me step by step how to solve this
I don't really know. I would hunt up the formula for the sum of an arithmetic series and see where that leads me.
http://www.trans4mind.com/personal_development/mathematics/series/sumNaturalNumbers.htm
natural number sequence is 1, 2, 3, 4, 5,/// notice that "0" is not a natural number
this is an arithmatic sequence of difference "1" so, \[S_n={n\over2}[a_0+(n-1)d]\\ S_n={n\over2}[1+(n-1)]\\ S_n={n^2\over2}\]
can you explain how you came up with the formula
the formula \[S_n={n\over2}[a_0+(n-1)d]\] is the formula for the sum of "n" numbers in arithmetic series starting from "a0" with a common difference of "d"