Hello thisismyname!
1^(-1) * 2^(-1) + 3^(-1) * 4^(-1) + 4^(-1) * 5^(-1) + 5^(-1) * 6^(-1) + 6^(-1) * 7^(-1) +...+ (p-2)^(-1) * (p-1)^(-1)
= 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 +.....+ (p-2)^(-1) * (p-1)^(-1)
This is the sum of the reciprocals of the square numbers p k to p.
Unfortunately, I know only the formula for the limit of all.
.
A rectangle number or pronische number p, is a number that is the product of two successive natural numbers.
The first square-wave numbers p are 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110
The sum of the reciprocals of all square numbers k = \(\frac{1}{p} \) is 1.
\(\sum\limits_{k=1}^{\infty }\frac{1}{k^{2}+k } =1\)
For my English I apologize.
Greeting asinus :- ) 
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