Question

write the common ratio of series 1/b³,1/b,b,b³​

Answer 1

x=1+a+a2+a3+⋯x=1+a+a2+a3+⋯

y=1+b+b2+b3+⋯y=1+b+b2+b3+⋯

Letz=1+ab+a2b2+a3b3+⋯Letz=1+ab+a2b2+a3b3+⋯

∵a and b are proper fractions∵a and b are proper fractions

∴a<1andb<1∴a<1andb<1

x=1+a+a2+a3+⋯is the sum of an infinite geometric progressionx=1+a+a2+a3+⋯is the sum of an infinite geometric progression

with first term 1 and common ratioa<1with first term 1 and common ratioa<1

∴sum x=a1−r=11−a∴sum x=a1−r=11−a

y=1+b+b2+b3+⋯is the sum of an infinite geometric progressiony=1+b+b2+b3+⋯is the sum of an infinite geometric progression

with first term 1 and common ratiob<1with first term 1 and common ratiob<1

∴sum y=a1−r=11−b∴sum y=a1−r=11−b

z=1+ab+a2b2+

Answer 2

Answer:

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