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
