Problem:
Geometric and arithmetic series, pulleys in parallell
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?