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Question

The value of limn(15)log514+18+116+... is?

A
2
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B
4
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C
8
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D
0
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Solution

The correct option is A 4
limn(15)log5(14+18+116+....)

=limn(15)log5⎜ ⎜ ⎜ ⎜ ⎜ ⎜141112⎟ ⎟ ⎟ ⎟ ⎟ ⎟

because 14+18+116+.... (infinite GP sum)

=a1r=141112
=12

limn(15)log51212=limn(15)2log512 ........... Using logbna=1nlogba
=limn15log514 .......... Using rlogba=logbar

=limn114=4


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