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Differential Calculus> If the sum of first n natural numbers is ...

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If the sum of first n natural numbers is 1/5 times the sum of their squares, then th value of n is

VIJAY KUMAR , 8 Years ago

Grade 11

1 Answers

Ajay

Last Activity: 8 Years ago

This question should have been posted in algebra section . Anyway here is solution.

It was easy, wonder why you cant do it

$sum\quad of\quad n\quad natural\quad numbers\quad =\quad \frac { n(n+1) }{ 2 } \\ Sum\quad of\quad squares\quad of\quad n\quad natural\quad numbers\quad =\quad \frac { n(n+1)(2n+1) }{ 6 } \\ Given\quad \frac { n(n+1) }{ 2 } \quad =\quad \frac { 1 }{ 5 } \left( \frac { n(n+1)(2n+1) }{ 6 } \right) \\ solving\quad for\quad n,\quad n\quad =7$

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