# Geometric and arithmetic series, pulleys in parallell

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Resistances in series can be reduced to a unique resistance R such that

eq(1) R= r1 + r2 +...+ rn

in Parallel , we have

eq (2) 1/ (1/r1 +1/r2 +...+ 1/rn)

For the pulleys , to reduce the effort to keep a block and tackle (which has a mass M at he end) in equilibrium , the necessary force F to furnish is :

eq(3) F = W/2^n

Where n is the number of pulleys

By comparing the two examples we notice that eq(1) is an arithmetic series

Whereas eq(3) is a geometric series

Then find the equivalent relation of eq(2) but this time for a geometric series. To be clearer what would be a mathematical relation to represent in equation a "parallel" pulleys system.

Still to say it in another way ,

(2) is to (1)

what

"a certain equation" would be to (3)

What would be this equation?

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For equation (2), when each pulley carries a weight of W, each pulley will reduce the force ...

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