Question

calculati suma 43+50+57+........+743 Va rog ajutatima!!

Answer 1

ai rezolvarea in poza

Answer 2

$43+50+57+...+743 = \\ \\ = \sum\limits_{k=6}^{106}(7k+1) = \sum\limits_{k=1}^{101}\Big(7(k+5)+1\Big) = \sum\limits_{k=1}^{101}7(k+5) + \sum\limits_{k=1}^{101}1 = \\ \\ = 7\cdot \sum\limits_{k=1}^{101}(k+5)+101 = 7\cdot \Big(\sum\limits_{k=1}^{101}k+\sum\limits_{k=1}^{101}5\Big)+101 = \\ \\ =7\cdot \Big(1+2+3+...+101+5\cdot 101\Big)+101 = \\ \\ = 7\cdot \Big(\dfrac{101\cdot 102}{2}+5\cdot 101\Big)+101 = \\ \\ = 7\cdot \Big(101\cdot 51+5\cdot 101\Big)+101 =$
$= 7\cdot \Big(101\cdot(51+5)\Big)+101 = \\ \\ = 7\cdot (101\cdot 56)+101 = \\ \\ = 7\cdot 101\cdot 56+101 = \\ \\ =101\cdot(7\cdot 56+1) = \\ \\ =101\cdot (392+1) = \\ \\ =101\cdot 393 = \\ \\ = 39693$