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How to write an embedded sum series in Wolfram Alpha?

Posted 2 months ago
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I am trying to write the following mathematical expression on wolfram alpha but failing , i do not know how to embedded the sum series into another as per the expression.

EQUATION

here is what i have so far:

[(2^k87^(2k))/(622^(2k)k!)[1-exp(-215^2/622^2)sum ((2^j15^(2j))/(622^(2j)*j!)), j=0 to k]]

inserting this into wolfram alpha i get:

WOLFRAM ALPHA EQUATION

i dont know how to add the other sum term into the expression... note: d=87 w=622 a=15

POSTED BY: Zak Ali
2 Replies
Posted 2 months ago

I wasn't able to do the nested sum in a single step, but breaking it into two slightly simpler nested sums might be valid. I also wasn't able to sum k from zero to infinity in the second summation without it timing out or saying that it could not understand my input, but summing k from zero to 20 looks like that is very very close to the infinite sum, even k from 0 to 6 gives almost the same result..

Sum[2^k 87^(2 k)/(622^(2 k) k!)*1, {k,0,Infinity}]+
Sum[2^k 87^(2 k)/(622^(2 k) k!)*-Exp[-215^2/622^2]*Sum[2^j*15^(2*j)/(622^(2*j) j!), {j,0,k}], {k,0,20}]

See if you can understand how I rearranged that and if you think you can justify the changes I made..

POSTED BY: Bill Nelson
Posted 2 months ago

Thanks a bunch! that works! Spent like 5 hours yesterday on it...

POSTED BY: Zak Ali
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