Is there a name for the way parallel resistors (and others) are added? I find this formula appears often in physics,
To add resistors in parallel, we do $\frac{1}{R_e}=\frac{1}{R_1}+\frac{1}{R_2}+...$
To add springs in series, we do $\frac{1}{k_e}=\frac{1}{k_1}+\frac{1}{k_2}+...$
To add capacitance in series, we do $\frac{1}{C_e}=\frac{1}{C_1}+\frac{1}{C_2}+...$
Is there a name for the method where variables are added to find an equivalence,  follow this pattern? Currently I would say "We find equivalent parallel resistance by taking the reciprocal sum of the resistances", but I winged this my self on the spot and I think "reciprocal sum" could be misleading(e.g. $R_e=\frac{1}{R_1}+\frac{1}{R_2}+...$) to someone who doesn't know whats been talked about already. Some similar ideas like root mean square have names, is there a name given to this method?
 A: It is called harmonic mean by mathematicians https://en.wikipedia.org/wiki/Harmonic_mean
A: It is called "parallel addition" or "parallel sum". See Anderson and Duffin's Series and parallel addition of matrices.
See also Ellerman's Introduction to Series-Parallel Duality.
Others have written about this, too. See Kent E. Erickson, "A New Operation for Analyzing Series-Paralled Networks," IRE Trans. on Circuit Theory, March 1959, pp.124-126.
A: “Parallel sum” is the name for that type of adding-up
R_tot = the parallel sum of the R_i’s
R_tot = 1 / ( 1/R_1 + 1/R_2 + ... 1/R_N )
——————
But alternatively, theres always a name for the reciprocal, and those add-up to the equivalent parallel value:
1/R = G, conductance of a resistor. Sum of conductances is total conductance, if parallel
1/k = c, compliance of a spring...
1/C = S, elastance of a capacitor...
Ive always thought these even exist for people who work with them a lot to not have to say “one over” or “parallel sum” etc. Or if considering whether to add something to a design can say “what’s its (eg) elastance?”, knowing immediately how much it will add to the parallel sum
