Question

Calculati suma tuturor numerelor naturale,care impartite la 2014 dau catul 55.

Answer 1

In primul rand, notam termenii in felul urmator : n, n+1, n+2,..., n+2013.
Astfel:

n : 2014 = 55
( n + 1 ) : 2014 = 55 rest 1
...
( n + 2013 ) : 2014 = 55 rest 2013.

( Am presupus ca sunt 2014 numere )

Deci:
=> n = 2014 * 55 = 110770

Calculam suma n + ( n + 1 ) +...+ ( n + 2013 ) = 110770 * 2014 + 2013 * 2014 : 2
=> Suma = 223090780 + 2027091 = 225117871

Sper ca te-am ajutat!

Answer 2

n= 2014·55+r    r∈{0,1,2,3,4,.....2013)  n∈{110770,110771,110772 110773.........112783}

S = 110770+(110770+1)+(110770+2)+...... ......+(110770+2013)  = 110770·2014 +(1+2+3+......+2013) =110770·2014+2013·2014/2 = 223090780+2027091 = 225117871