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Let S(n) = 1 + q + q^(2) +...+ q^(n) and...

Let `S_(n) = 1 + q + q^(2) +...+ q^(n) and T_(n) = 1 + ((q +1)/(2)) + ((q +1)/(2)) + ...+ ((q +1)/(2))^(n)`, where q is a real number and `q != 1`. If
`.^(101)C_(1) + .^(101)C_(2).S_(1) + ...+ .^(101)C_(101).S_(100) = alpha T_(100)`, then `alpha` is equal to

A

`2^(100)`

B

200

C

`2^(99)`

D

202

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The correct Answer is:
A
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