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The series x^2 + 2^2/(3cdot4)x^4+(2^2cdo...

The series `x^2 + 2^2/(3cdot4)x^4+(2^2cdot4^2)/(3cdot4cdot5cdot6)x^6+ (2^2cdot4^2cdot6^2)/(3cdot4cdot5cdot6cdot7cdot8)x^8+`... is-

A

Convergent, if `x^2 gt 1 ` and `divergent, if `x^2 le 1`

B

Convergent, if `x^2 le 1 ` and `divergent, if `x^2 gt 1`

C

Convergent, if `x^2 lt 1 ` and `divergent, if `x^2 ge 1`

D

Convergent, if `x^2 ge 1 ` and `divergent, if `x^2 lt 1`

Text Solution

Verified by Experts

The correct Answer is:
B
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