Question

A)1 supra 11 + 2 supra 11 + ..... + 10 supra 11.




B) 2 supra 15 + 4 supra 15 + ....+ 30 supra 15




C) 5 supra 7 + 10 supra 7 + .... + 35 supra 7

Answer 1

a)1/11 + 2/11 + ... +10/11 = 1+2+...+10 / 11=[10×(10+1)]:2 /11 = (10×11):2 / 11= 110:2 / 11= 55 / 11 amplific cu 11 = 5/1
b)2/15 + 4/15 + ... + 30/15=2×1+2×2+2×15 / 15= 2×(1+2+...+15) /15= 2× {[15×(15+1)]:2} /2= 2× [(15×16):2) / 15 = 2× (240 :2) / 15 = 2×120 /15 = 240 /15 amplificam cu 15 = 16/1
c)5/7+10/7+...+35/7=5×1+5×2+...+5×7 / 7 = 5×(1+2+...+7) /7 = 5×{[7×(7+1)]:2} /7= 5×[(7×8):2] /7 = 5×(56:2) / 7 = 5×28 / 7 = 140 / 7 amplific cu 7 = 20/1


Succes!!! Sper sa intelegi !!! Am folosit "Suma lui Gauss"