{an} and (bn} be two sequences given by an=(x)^1/2^n + (y)^1/2^n and bn=(x)^1/2^n - (y)^1/2^n for all n belongs to - Maths - Sequence and Series

Question

{an} and (bn} be two sequences given by an=(x)^1/2^n + (y)^1/2^n
and bn=(x)^1/2^n - (y)^1/2^n for all n belongs to N then a1*a2*a3
an is equal to

Ajanta Trivedi · Accepted Answer

given:
an=(x)1/2n+(y)1/2n   and bn=(x)1/2n-(y)1/2n  
therefore
an bn=(x)1/2n+(y)1/2n  
(x)1/2n-(y)1/2n  =(x)1/2n2-(y)1/2n  2=x1/2n-1-y1/2n-1=bn-1
then
a1*a2*a3* *an=∏r=1nar=∏r=1nar
brbr=∏r=1nbr-1br=b0b1*b1b2*b2b3* *br-1br=b0bn=x-ybn

hope this helps you

{an} and (bn} be two sequences given by an=(x)^1/2^n + (y)^1/2^n and bn=(x)^1/2^n - (y)^1/2^n for all n belongs to N then a1*a2*a3........an is equal to

{an} and (bn} be two sequences given by an=(x)^1/2^n + (y)^1/2^n and bn=(x)^1/2^n - (y)^1/2^n for all n belongs to N then a1a2a3........an is equal to