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Explanation:

We need to check options.

Option (a)π21π+1-π2
12+π2-π2 = 12 = 0.5 (terminating)

Option (b): sin21° + sin22° + … + sin288° + sin289°
= sin21° + sin22° + …  +  sin245° + … + cos22° + cos21°
= 44 + ½ = 44.5 (terminating)

Option (c)72933+227 
93+227 = 3 + 22/7 (terminating)

Option (d)4-π[1+π4+π42+π43+... inifinite terms]
4-π11-π4 = 4 (non-terminating)

Option (e)232-42+3
= 6 - 4 + √3 = 2 + √3 (non-terminating and non-repeating)

Hence, option (e).

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