Looking closely at the infinite series summation_n=1^infinity, it would be reaso

Question

Looking closely at the infinite series summation_n=1^infinity, it would be reasonable (and correct) to conclude that it diverges. However, it may be surprising that the similar infinite series summation_n=1^infinity 1/n^2 does not n= 1 diverge, instead converging to a number (albeit irrational): 1.645. In similar fashion, when reciprocals of the factorials are added together, they also produce a series that converges to an important (and irrational) number with which you are probably familiar: r (Euler's number). Another convergent series is that of the reciprocals of the Fibonacci numbers, which sum to produce another irrational number called the reciprocal Fibonacci constant, or psi. (As an aside, note that the Fibonacci series-and thus psi-are intimately related to the golden ratio phi 1.61803. Write a MATLAB script named PP1_P3a that calls your function get_fac to estimate e. Write a MATLAB script named PP1_P3B that calls your function get_fib to estimate psi. Your estimates must be to at least 10 decimal places.

Explanation / Answer

Good wishes,

First the code for sum of the reciprocals of factorials:

n=100

s=0

for i= 1:n

s = s + ( 1/ factorial(i) )

end

disp(s)

Next code for sum of reciprocals of fibnocci series:

s=(1/1) + (1/1)

n=100

a=1

b=1

for i = 1:n

s= s + ( 1 / (a+b) )

c=a

a=b

b=c+a

end

disp(s)

Explaination:

I have given the code in most simple manner and so hope it self explainatory.

Hope this is clear.

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