Binomial theorem and differential
本帖最後由 數學小子 於 5-3-2011 20:19 編輯1) Prove for n>0, that
sum(k=1 to n){1/k! product(r=0 to k-1)}<2
2) Find d/dx {f1(x)f2(x)f3(x)...fn(x)} 本帖最後由 -終場ソ使者- 於 6-3-2011 23:16 編輯
1)
Since
http://upload.wikimedia.org/math/a/a/5/aa537ff797e0ba9bac5384c6dcaf15de.png
http://upload.wikimedia.org/math/d/c/c/dccea0425688e6c7bec43e861ec485ea.png
http://upload.wikimedia.org/math/f/4/b/f4b23288e1c051c5c5edb1c6efc9c80e.png,
You prove http://upload.wikimedia.org/math/9/6/4/964833a0f869feca36d0188a05a29235.png,
...
iehttp://upload.wikimedia.org/math/8/1/d/81d15a8a449d9124acf7efbe159ee17a.png
2)http://upload.wikimedia.org/math/6/8/9/689527bc753d3683696962ca1a0f89e8.pnghttp://upload.wikimedia.org/math/4/7/3/4739aaa8eb14f74efaf7bb4294057b5b.png
http://upload.wikimedia.org/math/9/0/2/9026ae6cde6fc2255ee45042bb8f283c.png
http://upload.wikimedia.org/math/d/7/e/d7e608916f797f03de04e0f8ba791533.png
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