56.5K Shares
twitter facebook tumblr reddit quora medium
Share to Quora
Successfully copied the web link. You cloud share these fun content to quora!
3.) $a_{n}=-\frac{5}{n}$

3.) $a_{n}=-\frac{5}{n}$

Actualizado en

Question

3.) an=5na_(n)=-(5)/(n)

Best Answer

Step 1 - Write the sequence starting from index 1:
The sequence terms are:
a1=5a_(1)=-5
a2=52a_(2)=-(5)/(2)
a3=53a_(3)=-(5)/(3)
a4=54a_(4)=-(5)/(4)
......
an=5na_(n)=-(5)/(n)
Step 2 - We can find the Sum of the first n terms of the sequence using the formula:
Sn=i=1naiS_(n)=sum_(i=1)^(n)a_(i)
By substituting the value of an=5na_(n)=-(5)/(n), we solve for the formula of SnS_(n).
Sn=5(11+12+13+...+1n)S_(n)=-5((1)/(1)+(1)/(2)+(1)/(3)+...+(1)/(n))
Step 3 - Simplify the formula by using the Harmonic Number formula:
Hn=k=1n1kH_(n)=sum_(k=1)^(n)(1)/(k)
Sn=5Hn+5S_(n)=-5H_(n)+5
Step 4 - Write the final answer:
Sn=5Hn+5S_(n)=-5H_(n)+5
Answer: Sn=5Hn+5S_(n)=-5H_(n)+5
Harmonic Number and Sequence Summation in Series