Recurring sequence

[A13235378]

A sequence {an} of real numbers is defined by:

[MATH]a_1=1,a_{n+1}=1+a_1.a_2.a_3...a_n,n\geq 1 [/MATH]
prove that :

[MATH]\sum_{n=1}^{\infty }\frac{1}{a_n}=1 [/MATH]

 

[tkhunny]

Can you write out the first three terms?

 

[Deleted member 4993]

A sequence {an} of real numbers is defined by:

[MATH]a_1=1,a_{n+1}=1+a_1.a_2.a_3...a_n,n\geq 1 [/MATH]
prove that :

[MATH]\sum_{n=1}^{\infty }\frac{1}{a_n}=1 [/MATH]

If I were to do this problem, I would attempt to use method of induction.

Please show us what you have tried and exactly where you are stuck.

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