Question

Calculati: (7^1×7^6×7^11×....×7^301):(7^1×7^4×7^7×7^10×....×7^154)​

Answer 1

Răspuns:

Explicație pas cu pas:

a)N=7^(1+6+11+...+301)=7^∑(5k+1)         ∑ de la 1 la 60⇒n=60; ∑k=(a1+an)×n/2

=7^(5∑k+60)=7^[5×(1+60)×60/2+60]=7^(150×61+60)=7^(9150+60)=7^9210

b)

N=7^(1+4+7+....+154)=7^(∑3k+1)   k:1⇒51   ∑k=suma Gauss sau suma unei progresii aritmetice cu r=1

N=7^(3∑k+51)=7^[3×(1+51)×51/2+51]=7^(3×26×51+51)=7^(3978+51)=7^4029