lambs = seq(0.01, 0.2, length.out=200)

lhs = function(lam, n=15){
    one_plus_lambda = 1 + lam
    one_plus_lambda_to_the_n = one_plus_lambda^n 
    
    1/one_plus_lambda_to_the_n + (0.1/lam) * ( 1 - 1/one_plus_lambda_to_the_n ) 
}

# Find the value of lambda where lhs(lambda)=1.05:
# 
source('http://waxworksmath.com/Authors/A_F/Conte/Code/Chapter3/utils.R')

rt = bisection_method(0.05, 0.10, function(x){ lhs(x) - 1.05 })
print(rt)

# Plot the left-hand-side and this value of lambda:
# 
plot(lambs, lhs(lambs), type='l', xlab='lambda', ylab='left-hand-side')
abline(h=1.05, col='blue')
abline(v=rt[1], col='green')
grid()