![For integers n and r, let ([n], [r])={(""^nCr," ""if " n ge r ge 0), (0," ""otherwise"):}. The maximum value of k for which the sum sum(i=0)^(k)([10], [i])([15], [k-i])+sum(i=0)^(k+1)([12], [i])([13], [k+1-i])exists, is](https://d10lpgp6xz60nq.cloudfront.net/web-thumb/647045415_web.png "For integers n and r, let ([n], [r])={(\"\"^nCr,\" \"\"if \" n ge r ge 0), (0,\" \"\"otherwise\"):}. The maximum value of k for which the sum sum(i=0)^(k)([10], [i])([15], [k-i])+sum(i=0)^(k+1)([12], [i])([13], [k+1-i])exists, is")
For integers n and r, let ([n], [r])={(""^nCr," ""if " n ge r ge 0), (0," ""otherwise"):}. The maximum value of k for which the sum sum(i=0)^(k)([10], [i])([15], [k-i])+sum(i=0)^(k+1)([12], [i])([13], [k+1-i])exists, is
The set representing the correct order of first ionisation potential is:
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