Leta1,a2,a3,....,a10be in G.P. witha1>0fori=1,2,...10andSbe the set of pairs(r,k),rk∈N(the set of natural numbers) for which∣∣∣∣∣logear1ak2logear2ak3logear3ak4logear4ak5logear5ak6logear6ak7logear7ak8logear8ak9logear9ak10∣∣∣∣∣=0Then the number of elements inS, is :Infinitely many4102Leta1,a2,a3,....,a10be in G.P. witha1>0fori=1,2,...10andSbe the set of pairs(r,k),rk∈N(the set of natural numbers) for which∣∣∣∣∣logear1ak2logear2ak3logear3ak4logear4ak5logear5ak6logear6ak7logear7ak8logear8ak9logear9ak10∣∣∣∣∣=0Then the number of elements inS, is :Infinitely many4102a1,a2,a3,....,a10a1,a2,a3,....,a10a1,a2,a3,....,a10a1aaa111,,a2aaa222,,a3aaa333,,........,,a10aaa1010101010a1>0a1>0a1>0a1aaa111>>00i=1,2,...10i=1,2,...10i=1,2,...10ii==11,,22,,.....10.10SSSSS(r,k),rk∈N(r,k),rk∈N(r,k),rk∈N((rr,,kk)),,rrkk∈∈NN∣∣∣∣∣logear1ak2logear2ak3logear3ak4logear4ak5logear5ak6logear6ak7logear7ak8logear8ak9logear9ak10∣∣∣∣∣=0∣∣∣∣∣logear1ak2logear2ak3logear3ak4logear4ak5logear5ak6logear6ak7logear7ak8logear8ak9logear9ak10∣∣∣∣∣=0∣∣∣∣∣logear1ak2logear2ak3logear3ak4logear4ak5logear5ak6logear6ak7logear7ak8logear8ak9logear9ak10∣∣∣∣∣=0∣∣∣∣∣logear1ak2logear2ak3logear3ak4logear4ak5logear5ak6logear6ak7logear7ak8logear8ak9logear9ak10∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣logear1ak2logear2ak3logear3ak4logear4ak5logear5ak6logear6ak7logear7ak8logear8ak9logear9ak10logear1ak2logear2ak3logear3ak4logear4ak5logear5ak6logear6ak7logear7ak8logear8ak9logear9ak10logear1ak2logear2ak3logear3ak4logear1ak2logear1ak2logelogloglogeeear1aaar1rrr111ak2aaak2kkk222logear2ak3logear2ak3logelogloglogeeear2aaar2rrr222ak3aaak3kkk333logear3ak4logear3ak4logelogloglogeeear3aaar3rrr333ak4aaak4kkk444logear4ak5logear5ak6logear6ak7logear4ak5logear4ak5logelogloglogeeear4aaar4rrr444ak5aaak5kkk555logear5ak6logear5ak6logelogloglogeeear5aaar5rrr555ak6aaak6kkk666logear6ak7logear6ak7logelogloglogeeear6aaar6rrr666ak7aaak7kkk777logear7ak8logear8ak9logear9ak10logear7ak8logear7ak8logelogloglogeeear7aaar7rrr777ak8aaak8kkk888logear8ak9logear8ak9logelogloglogeeear8aaar8rrr888ak9aaak9kkk999logear9ak10logear9ak10logelogloglogeeear9aaar9rrr999ak10aaak10kkk1010101010∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣==00SSSSSInfinitely many444444101010101010222222A4444444B2222222CInfinitely manyInfinitely manyD10101010101010?<p></p>

Leta1,a2,a3,....,a10be in G.P. witha1>0fori=1,2,...10andSbe the set of pairs(r,k),rk∈N(the set of natural numbers) for which∣∣∣∣∣logear1ak2logear2ak3logear3ak4logear4ak5logear5ak6logear6ak7logear7ak8logear8ak9logear9ak10∣∣∣∣∣=0Then the number of elements inS, is :Infinitely many4102Leta1,a2,a3,....,a10be in G.P. witha1>0fori=1,2,...10andSbe the set of pairs(r,k),rk∈N(the set of natural numbers) for which∣∣∣∣∣logear1ak2logear2ak3logear3ak4logear4ak5logear5ak6logear6ak7logear7ak8logear8ak9logear9ak10∣∣∣∣∣=0Then the number of elements inS, is :Infinitely many4102a1,a2,a3,....,a10a1,a2,a3,....,a10a1,a2,a3,....,a10a1aaa111,,a2aaa222,,a3aaa333,,........,,a10aaa1010101010a1>0a1>0a1>0a1aaa111>>00i=1,2,...10i=1,2,...10i=1,2,...10ii==11,,22,,.....10.10SSSSS(r,k),rk∈N(r,k),rk∈N(r,k),rk∈N((rr,,kk)),,rrkk∈∈NN∣∣∣∣∣logear1ak2logear2ak3logear3ak4logear4ak5logear5ak6logear6ak7logear7ak8logear8ak9logear9ak10∣∣∣∣∣=0∣∣∣∣∣logear1ak2logear2ak3logear3ak4logear4ak5logear5ak6logear6ak7logear7ak8logear8ak9logear9ak10∣∣∣∣∣=0∣∣∣∣∣logear1ak2logear2ak3logear3ak4logear4ak5logear5ak6logear6ak7logear7ak8logear8ak9logear9ak10∣∣∣∣∣=0∣∣∣∣∣logear1ak2logear2ak3logear3ak4logear4ak5logear5ak6logear6ak7logear7ak8logear8ak9logear9ak10∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣logear1ak2logear2ak3logear3ak4logear4ak5logear5ak6logear6ak7logear7ak8logear8ak9logear9ak10logear1ak2logear2ak3logear3ak4logear4ak5logear5ak6logear6ak7logear7ak8logear8ak9logear9ak10logear1ak2logear2ak3logear3ak4logear1ak2logear1ak2logelogloglogeeear1aaar1rrr111ak2aaak2kkk222logear2ak3logear2ak3logelogloglogeeear2aaar2rrr222ak3aaak3kkk333logear3ak4logear3ak4logelogloglogeeear3aaar3rrr333ak4aaak4kkk444logear4ak5logear5ak6logear6ak7logear4ak5logear4ak5logelogloglogeeear4aaar4rrr444ak5aaak5kkk555logear5ak6logear5ak6logelogloglogeeear5aaar5rrr555ak6aaak6kkk666logear6ak7logear6ak7logelogloglogeeear6aaar6rrr666ak7aaak7kkk777logear7ak8logear8ak9logear9ak10logear7ak8logear7ak8logelogloglogeeear7aaar7rrr777ak8aaak8kkk888logear8ak9logear8ak9logelogloglogeeear8aaar8rrr888ak9aaak9kkk999logear9ak10logear9ak10logelogloglogeeear9aaar9rrr999ak10aaak10kkk1010101010∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣==00SSSSSInfinitely many444444101010101010222222A4444444B2222222CInfinitely manyInfinitely manyD10101010101010?

Eduprobe

Question:

Solution: