Question

Calculati: E(2) + E(3) +.....+ E(100)
Știind că E(x)= 1/(x-1)•x

Answer 1

= 1/2(2-1). + 1/3(3-1). + 1/4(4-1)+. ..+ 1/100(100-1) = 1/2x1 + 1/3x2 + 1/4x3 + ....+ 1/100x 99 = 1/2x1. + 1/3x2 + 1/4x3. + ....+1/100x 99; pe 1 de la numarator il scrim ca : 2-1= 3-2= 4-3...= 100-99; si vom avea ( 2-1)/2x1. + (3-2)/2x3 + (4-3)/4x3 +....+ (100-99)/100x99 = 2/2x1 - 1/2x1 + 3/2x3 -2/2x3 + 4/4x3- 3/4x3 +. + 100/100x99- 99/100x99= 1- 1/2 + 1/2 -1/3 + 1/3 -1/4+....+ 1/99-1/100= 1-1/100= 99/100