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SUM.LI
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1991-10-28
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677b
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23 lines
sum(n) = n*(n+1)/2
sum(n^2) = n*(n+1)*(2*n+1)/6
sum(n^3) = n^2*(n+1)^2/4
sum((-1)^(n-1)*n^2) = (-1)^(n-1)*n*(n+1)/2
sum(2*n) = n*(n+1)
sum(2*n-1) = n^2
sum((2*n-1)^2) = n*(4*n^2-1)/3
sum((2*n-1)^3) = n^2*(2*n^2-1)
sum(j!*j, j from 1 to n) = (n+1)!-1
sum(j/(j+1)!, j from 1 to n) = 1-1/(n+1)!
sum(1/(j!*(n-j)!), j from 0 to n) = 2^n/n!
sum(1/n!, n from 0 to inf) = e
sum((-1)^n/n!, n from 0 to inf) = 1/e
sum(x^n/n!, n from 0 to inf) = e^x
sum((-1)^n*x^(2*n+1)/(2*n+1)!, n from 0 to inf) = sin(x)
sum((-1)^n*x^(2*n)/(2*n)!, n from 0 to inf) = cos(x)
sum(x^(2*n+1)/(2*n+1)!, n from 0 to inf) = sinh(x)
sum(x^(2*n)/(2*n)!, n from 0 to inf) = cosh(x)
end