# Partial Sums of Infinite Series

Partial sums of infinite series play a crucial role in the realm of mathematics, particularly in the study of calculus and analysis. When dealing with infinite series, it's often impractical to compute the sum directly. Instead, mathematicians turn to partial sums, which involve summing only a finite number of terms. These partial sums provide valuable insights into the behavior and convergence of the series, enabling mathematicians to make precise statements about the behavior of functions and the nature of infinity. In this essay, we will delve into the concept of partial sums and explore their significance in mathematical analysis.

Questions

- How do you find the n-th partial sum of an infinite series?
- How do you find the limit of #s(n)=64/n^3[(n(n+1)(2n+1))/6]# as #n->oo#?
- How do you find the nth partial sum, determine whether the series converges and find the sum when it exists given #1+1/3+1/9+...+(1/3)^n+...#?
- How do you find the nth partial sum, determine whether the series converges and find the sum when it exists given #ln(4/3)+ln(9/8)+ln(16/15)+...+ln(n^2/(n^2-1))+...#?
- How do you find a formula for the nth partial sum of the series [5/1*2]+[5/2*3]+[5/3*4]+...+[5/n(n+1)]+... and use it to find the series' sum if the series converges?
- How do you find partial sums of infinite series?
- Is it possible to evaluate #sum_(n=1)^oosqrt(4n^2x^2-1)/(4n^2)# in terms of #x#?
- How do you find the 4-th partial sum of the infinite series #sum_(n=1)^oo(3/2)^n# ?
- Maths is this questions answer below?
- How do you find the sum of #2/1+4/3+8/9+16/27+...+2^(n+1)/3^n+...#?
- How do you find the nth partial sum, determine whether the series converges and find the sum when it exists given #1-1/3+1/9-...+(-1/3)^n+...#?
- How do you find the 10-th partial sum of the infinite series #sum_(n=1)^oo(0.6)^(n-1)# ?
- How do you find the sum of #ln ( 1 + 1 / (2^(2^n)) )# from n=0 to infinity? Thanks!?
- How do you find the limit of #s(n)=81/n^4[(n^2(n+1)^2)/4]# as #n->oo#?
- Can anyone find the value and if possible show every step? Thanks in advance.
- For the sequence 1/3, 1/3^2 ,1/3^3 ,1/3^4 ,1/3^5,…, ?
- How do you find the sum of #(1+1)+(1/3+1/5)+(1/9+1/25)+...+(3^-n+5^-n)+...#?
- How do you find the 6-th partial sum of the infinite series #sum_(n=1)^oo1/n# ?
- How do you find the nth partial sum, determine whether the series converges and find the sum when it exists given #1/(1*3)+1/(3*5)+1/(5*7)+...+1/((2n-1)(2n+1))+...#?
- How do you find the limit of #s(n)=1/n^2[(n(n+1))/2]# as #n->oo#?