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Let S n = 1 + q + q 2 + ... + q n and T n = 1 + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + 2 1 q + 2 2 1 q ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + ... + n 2 1 q ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + where q is a real number and q ≠ 1. If 101 C 1 + 101 C 2 . S 1 + .... + 101 C 101 . S 100 = α T 100 then α is equal to

1. 202
2. 200
3. 2 100
4. 2 99

Correct answer: 2 100

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