Răspuns:
Explicație pas cu pas:
a)
1/1*2 = 1/1 - 1/2
1/2*3 = 1/2 - 1/3
1/3*4 = 1/3 - 1/4
................
1/99*100 = 1/99 - 1/100
_________________
1/1*2 + 1/2*3 + 1/3*4 + ... + 1/99*100 = 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/99 - 1/100 = 1/1 - 1/100 = 100/100 - 1/100 = 99/100
x*99/100 = 99
x = 99 : 99/100 = 99*100/99 = 100
b)
1 + 2 + 3 + ... + 50 = 50*51/2
partea din dreapta egalului se calculeaza dupa modelul de la punctul a)
1/1*2 + 1/2*3 + 1/3*4 + ... + 1/25*26 = 1/1 - 1/26 = 26/26 - 1/26 = 25/26
ecuatia devine
1/51*x*50*51/2 = 25/26
25*x = 25/26
x = 25/26 : 25 = 25/26*1/25 = 1/26
