Question

URGENT VA ROG DAU COROANA

Answer 1

Răspuns:

Explicație pas cu pas:

1)∑k(3k+1)=3∑k²+∑k   k=1.......n    n∈N

∑k=n(n+1)/2      ∑k²=n(n+1)(2n+1)/6

S=3×n(n+1)(2n+1)/6+n(n+1)/2 =n(n+1)/2×(2n+1+1)=2n(n+1)²/2=n(n+1)²

2)

1/(4n-3)(4n+1)=-1/4(4n-3)+1/4(4n+1)

S=-1/4+1/4(4n+1)=(4n+1-1)/4(4n+1)=4n/4(4n+1)=n/(n+1)

5)

progresie geometrica cu ratia q=1/2 cu n termeni:  S=b1×(q^n-1)/(q-1)

S=1/2×(1/2^n-1)/(1/2-1)=1/2×(1/2^n-1)/(-1/2)=1-1/2^n