Question

$\sum_{n=0}^{\infty}(-1)^{n}x^{2n} = \frac{1}{1+x^2}$, Note that as N becomes larger, the blue graph matches the red graph closer and closer on the interval of convergence -1 < x < 1 (highlighted in yellow), but outside of that interval, it does not. HW. Find the convergence interval Plot the sum of series using n=0 to 5, and compare it with the function $\frac{1}{1+x^2}$

          $\sum_{n=0}^{\infty}(-1)^{n}x^{2n} = \frac{1}{1+x^2}$,
Note that as N becomes larger, the blue graph matches the
red graph closer and closer on the interval of convergence
-1 < x < 1 (highlighted in yellow), but outside of that
interval, it does not.
HW.
Find the convergence interval
Plot the sum of series using n=0 to 5,
and compare it with the function $\frac{1}{1+x^2}$

∑n=0^∞(-1)^nx^2n = (1)/(1+x^2),
Note that as N becomes larger, the blue graph matches the
red graph closer and closer on the interval of convergence
-1 < x < 1 (highlighted in yellow), but outside of that
interval, it does not.
HW.
Find the convergence interval
Plot the sum of series using n=0 to 5,
and compare it with the function (1)/(1+x^2)

Added by Adam N.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Hemraj Kumawat

Step 1

Let's denote it as `f`. We will use a loop to calculate the sum from `n=0` to `N`. Second, we need to define the function `g = 1/(1+x^2)`. Third, we will plot both functions on the same graph for `x` in the range `-2` to `2`. We will use different colors for Show more…

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I need MATLAB code to graphically represent this function from n=0 to 20 and compare it with 1/(1+x^2). Note that as N becomes larger, the blue graph matches the red graph more closely on the interval of convergence -1 < x < 1, highlighted in yellow. However, outside of that interval, it does not. HW: Find the convergence interval. Plot the sum of the series using n=0 to 5.