Thread: exponential function on wikipedia

hi guys,

would some one be willing to explain this figure on the wikipedia's article:
Exponential function - Wikipedia, the free encyclopedia

"The exponential function (in blue), and the sum of the first n + 1 terms of the power series on the left (in red)." - the figure on the right, I don't understand what tries to say and especially I am interested to understand the meaning of the red curve

THANKS

Originally Posted by problady

hi guys,

would some one be willing to explain this figure on the wikipedia's article:
Exponential function - Wikipedia, the free encyclopedia

"The exponential function (in blue), and the sum of the first n + 1 terms of the power series on the left (in red)." - the figure on the right, I don't understand what tries to say and especially I am interested to understand the meaning of the red curve

THANKS

The graph of the blue line is e^x. The red curve is the individual tems of the summation, being added one at a time. I have no idea why they would include this except to show that the series does actually converge to e^x.

-Dan

Originally Posted by topsquark

The graph of the blue line is e^x. The red curve is the individual tems of the summation, being added one at a time. I have no idea why they would include this except to show that the series does actually converge to e^x.

-Dan

I think the idea is to show how fast the series converges. In fact, on the interval from –e to e, the graph of the sum of the first eight terms of the series is almost indistinguishable from the exponential graph.