Indian Institute of Foreign Trade 2017 Solved Paper

Question : 60 of 114

Marks: +1, -0

(1+5)\log_\e3 + (1+5^2)/2! (\log_\e3)^2 + (1+5^3) /3! (\log_\e3)^3 + ....

Solution:

Choice (B) Assume log

_\e 3

= x, then the series can be written as

( x + { x ^ { 2 } } /{ 2 ! } + { x ^ { 3 } }/ { 3 ! } + { x ^ { 4 } }/ { 4 ! } + ...)+ ( 5 x + { ( 5 x ) ^ { 2 } } /{ 2 ! } + { ( 5 x ) ^ { 3 } } /{ 3 ! } + .....)

= e ^ { x } - 1 + e ^ { 5 x } - 1 = e ^ { \log _ { e } 3 } - 1 + e ^ { 5 \log _ { e } 3 } - 1

= 3 - 1 + 3 ^ { 5 } - 1 = 244

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