Question

7 la puterea 11+12+...+30 = 7 la puterea 3n × 49
n=? Va rogg mult

Answer 1

7 la 11+12+13+...+30=30*31/2-10*11/2=930/2-110/2=465-55=410
       7 la 3n * 49 =7 la  3n * 7² =  7 la 3n +2 ⇒3n+2=410  ⇒ 3n  = 408 ⇒
⇒ n  =  136  cu placere

Answer 2

7¹¹⁺¹²⁺¹³⁺---⁺³⁰  = 7³ⁿ × 49

11+12+13+...30=(11+30)×(30-10)/2= 41×20/2=41×10=410

7⁴¹⁰= 7³ⁿ ₓ 7²
7⁴¹⁰=7³ⁿ⁺²
3n+2=410
3n=410-2
3n=408  |:3
n= 136