Question

Calculați :
a) 1×2+2×3+3×4+4×5+.....2010×2011
b) 5×10+10×15+15×20+.....+10050×10055​

Answer 1

Explicație pas cu pas:

a)  Suma e de forma k(k+1) = k^2 + k

Suma k^2 = k(k+1)(2k+1)/6      

S= 1+1 + 2^2+1 + 3^3+1 + 4^2+1 +.... +2010^2+2010

S= 2010*2011(4020+1)/6 = 2010*2011*4021/6 = 335*2011*4021

b)  Dam factor comun 5*5:

S1= 25(1*2 + 2*3 + 3*4 + 4*5 ....) = 25 * S = 25*335*2011*4021