1.

How many consecutive natural numbers from 1 should be added to get 465?

Answer»

Sum of first n natural numbers

\(\frac{n(n+1)}{2}=465\)

n2 + n = 930

\(n^2+n+\frac{1}{4}=930+\frac{1}{4}\)

\((n+\frac{1}{2}){^2}=\frac{3721}{4},n+\frac{1}{2}=\frac{61}{2}\)

n = 30

The sum of first 30 natural numbers = 465



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