If e^e^x = a0 + a1x^2 +a2x^2+ ..., then

If e^ex = a0 + a1x2 +a2x2+ …, then

(1) a0 = 1

(2) a0 = e

(3) a0 = ee

(4) a0 = e2

Solution:

Solution Paper Sequences JEE Exam

= 1+ (1/1!) (1 + x + x2/2! + ….) + (1/2!)(1 + 2x/1! + (2x)2/2! + ….)+..

= (1 + 1/1! + 1/2! + 1/3! +…) + x (1/1! + 2/2!1! + …)+….

So a0 = e

Hence option (2) is the answer.

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