Question

how to do partial sums in calculus

Answer 1

Answer:

This is the Sequence of even numbers from 2 onwards: {2, 4, 6, 8, 10, 12, ...}

This is the Partial Sum of the first 4 terms of that sequence: 2+4+6+8 = 20

Let us define things a little better now:

A Sequence is a set of things (usually numbers) that are in order.

Sequence

A Partial Sum is the sum of part of the sequence.

The sum of infinite terms is an Infinite Series.

And Partial Sums are sometimes called "Finite Series".

Sigma

Partial Sums are often written using Σ to mean "add them all up":

Σ This symbol (called Sigma) means "sum up"

So Σ means to sum things up ...

Sum What?

Sum whatever is after the Sigma:

Σ

n

so we sum n

But What Values of n ?

The values are shown below

and above the Sigma:

4

Σ

n=1

n