Question

how many consecutive natural numbers from 1 should be added to get 465​

Answer 1

1+2+3+...+n = n*(n+1)/2

where n is an integer and n+%3E=+1

Set this expression equal to 465 and solve

n(n+1)/2 = 465

n(n+1) = 2*465

n(n+1) = 930

n^2+n = 930

n^2+n-930 = 0

(n-30)(n+31) = 0

n-30 = 0 or n+31 = 0

n = 30 or n = -31

Since n+%3E=+1, then n = 30 is the only practical solution.

This means that the sum of the first 30 consecutive positive integers is equal to 465.

So,

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30 = 465....

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