(1) How can we find the partial sum of n1000 instantly ?
(2) is there is a simple method to find partial sum of the sequence f(n) ?
(3) Any general method to compute partial sum of sequence ?
(4) What is the value of Method , if we have good approximation for all differentable sequence ?
* it is possible gives a short approximation correct for many decimal places
Sn~ 1/1001[ (n+1/2)1001- (1/2)1001]
I think that if you just itegrate the function up to the appropriate
limit of n, then you get an approximate answer for the sum of the sequence. ie you integrate under the curve instead of summing over the rectangles.
@ Juan Weisz
That is more than that . It is a little secret have little secret of analytic continuity and discreetness of integers
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