#
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
#
#-----

partial_sum = function(N=100){
    # N = how many terms to sum from this series
    ti = 2 # the term index (start at the second term)
    S = 1 # the sum of all terms
    term_sign = -1
    number_of_terms_summed = 0
    number_of_terms_to_sum_before_changing_sign = 1
    #all_terms = c(S)
    
    while( ti <= N ){
        term = ( 1/ti ) * term_sign
        #all_terms = c( all_terms, 1/term ) # for debugging lets make sure that our terms look correct

        S = S + term
        ti = ti+1

        number_of_terms_summed = number_of_terms_summed + 1
        if( number_of_terms_summed >= number_of_terms_to_sum_before_changing_sign ){
            term_sign = -1 * term_sign
            number_of_terms_to_sum_before_changing_sign = number_of_terms_to_sum_before_changing_sign + 1
            number_of_terms_summed = 0
        }
    }
    return(S)
}

# Lets plot the sequence of partial sums as some value:
#
#postscript("../WriteUp/Graphics/exercise_4_1_part_k_sequence_of_partial_sums.eps", onefile=FALSE, horizontal=FALSE)

ns = 10^(1:7)
ss = c()
for( n in ns ){
    S = partial_sum(n)
    ss = c( ss, S )
}
plot( log(ns,10), ss, type='b', pch=20, cex=1.5, xlab='p: Number of terms=10^p', ylab='Partial Sum of 10^p terms' )
grid()

#dev.off()