infinite

x=1+a+a²+a³+...to infinity.(|a|<1)
y=1+b+b²+...to infinity.(|b|<1)
Prove that 1+ab+a²b²+a³b³+...to infinity=xy/x+y-1

2 Answers

Sum of n terms of a GP = a(1-rⁿ)/(1-r)

Now if lrl < 1 then the sum converges to a particular value. as lrl<1 so lim(nâ†’âˆž)rⁿ = 0 . So, the sum can be re-written as a/(1-r)

In 1st GP, a=1 and r=a

In 2nd GP, a=1 and r=b

thnx

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