How to find general formula for partial sums?

A Partial Sum is a sum of sart of a sequence, where a sequence is a set of things (usually numbers) that are in order.

Partial Sums are often written using Σ (called Sigma) to mean "add them all up":

When you should calculate the kth partial sum of an arithmetic sequence, you need to add the first k terms. If k is large, than you will need a long time to calculate the sum. Fortunately, you can use a general formula instead of plugging in each of the values for n. 

The first thing you should do is to find the first term of the sequence.

Then you should find the kth term of the sequence.

Then you should use the formula for the kth partial sum of an arithmetic sequence to find the sum.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

6/20

step-by-step explanation: