📚 How to test for convergence using the partial sum test with infinite series

What you'll need:

Partial sum test: (lim_(n→∞)⁡〖S_n=S〗 )

If the partial sums of an infinite series have a limit S, we say the series converges; otherwise it diverges.

Sum of n terms for geometric progression: ▭(s_n=(a(1−r^n))/(1−r))

A geometric sequence or geometric progression (GP) is one in which each term after the first is formed by multiplying the preceding term by a factor r, called the common ratio. For example, the common ratio for 2, 4, 8, 16 , … would be r=2.

Q. Does the following geometric series converge?

1+1/( 2 )+1/2^2 +1/2^3 +…+1/2^(n−1) +…