Sk=a1−r=k1−1k+1=k(k+1)k=k+1S_k = \frac{a}{1-r} = \frac{k}{1 - \dfrac{1}{k+1}} = \frac{k(k+1)}{k} = k+1Sk=1−ra=1−k+11k=kk(k+1)=k+1 ∑k=1nSk=∑k=1n(k+1)=n(n+1)2+n=n(n+3)2\sum_{k=1}^{n} S_k = \sum_{k=1}^{n} (k+1) = \frac{n(n+1)}{2} + n = \frac{n(n+3)}{2}∑k=1nSk=∑k=1n(k+1)=2n(n+1)+n=2n(n+3)