x=1+a+a2=......
x=1−a1⇒a=1−x1
y=1−b1⇒b=1−y1
z=1−c1⇒c=1−z1
a,b,c are in A.P.
⇒1−x1,1−y1,1−z1 are in A.P.
⇒−x1,−y1,−z1 are in A.P.
⇒x1,y1,z1 are in A.P.
If x=n=0∑∞an,y=n=0∑∞bn,z=n=0∑∞cn, where a,b,c are in A.P. and ∣a∣<1,∣b∣<1,∣c∣<1, abc=0, then
Held on 27 Jun 2022 · Verified 6 Jul 2026.
x,y,z are in A.P.
x,y,z are in G.P.
x1,y1,z1 are in A.P.
x1+y1+z1=1−(a+b+c)
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