let r be a real constant in the interval defined by 0

We used variables n.terms, i.vec, and r.const.

a.) Write a function called estimatePowerSeries with input r.const and n.terms, and output series.sum, which holds the value of the sum.

b). Add the following code to your script to make a table of estimates of the sum for a range of terms from 1 to 10 and letting r be 0.5 (r.test1):

r.test1

testPower

# function to use sapply for looping

c(i,round(estimatePowerSeries(r.const,i),digits=3))

}

# use sapply to loop over index i from 1 to 10

t(sapply(1:10,function(x){testPower(r.test1,x)}))

Note: we have not covered loops yet, so do not worry if you do not understand the code above. However, sapply repeats the function of x for values of x from 1:10 and stacks the results. round is a function that truncates the digits of a floating point number (a number with a decimal part/mantissa).

c). Repeat b) letting r be 0.8. For which value of r does the sum converge to the limit faster? Optional: explain why the faster convergence.

6. Write a function called calculateParallelResistance that computes and returns the total resistance of n resistors arranged in parallel according to the formula:

where R_T is the total resistance of the parallel system and R_k is the resistance of each resistor in the parallel system. The value of n is not needed for the code; it is implicit in the input, which is a vector of parallel resistance (resist.vec) in Ohms (). Take advantage of element-wise operations on the input vector and the built-in sum function for adding the elements of a vector.

b.) Test the function on an input vector of three resistors in parallel: c(200 470, 220).