Learn more. Asked 10 years, 6 months ago. Active 7 years, 9 months ago. Viewed 35k times. Srivatsan Danny King Danny King 1, 2 2 gold badges 18 18 silver badges 27 27 bronze badges. Add a comment. Active Oldest Votes. Nicolas Villanueva Nicolas Villanueva 5 5 silver badges 11 11 bronze badges. Did Did k 27 27 gold badges silver badges bronze badges. To explore much further this world of divergent series , a place to start might be mathoverflow.
We note the three disks overlap draw these three disks on a piece of paper. Jiangwei Xue Jiangwei Xue 2, 1 1 gold badge 13 13 silver badges 17 17 bronze badges.
That makes it somewhat clearer! Thank you. According to Euler, Let us say, therefore, that the sum of any infinite series is the finite expression, by the expansion of which the series is generated.
Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post.
Linked 3. Related 5. Hot Network Questions. So the 20 in the last line is found by adding together 10 and Each of the 10s in the line above are found by adding together a 6 and a 4. It is, of course, often impractical to write out Pascal"s triangle every time, when all that we need to know are the entries on the nth line. Clearly, the first number on the nth line is 1.
The second number is n. The third number is: n n - 1. In general, the rth number in the nth line is: n! The Binomial Theorem states that, where n is a positive integer:. This means use the Binomial theorem to expand the terms in the brackets, but only go as high as x 3.
The previous version of the binomial theorem only works when n is a positive integer.
0コメント