Let S_n = 1 + q + q^2 + ... + q^n and T_n = 1 + ((q+1)/2 ) + ((q+1)/2 )^2 + ... + ((q+1)/2 )^n, where q is a real number and q ≠ 1. If ^101C_1 + ^101C_2 · S_1 + ... + ^101C_101 · S_100 = α T_100, then α is equal to

Let S_n = 1 + q + q^2 + ... + q^n and T_n = 1 + ((q+1)/2 )… — JEE Main 2019 Mathematics PYQ

JEE Main 2019 · 11 Jan · Shift II

Let

S_n = 1 + q + q^2 + ... + q^n

and

T_n = 1 + \left(\frac{q+1}{2}\right) + \left(\frac{q+1}{2}\right)^2 + ... + \left(\frac{q+1}{2}\right)^n

, where

q

is a real number and

q \neq 1

. If

^{101}C_1 + ^{101}C_2 \cdot S_1 + ... + ^{101}C_{101} \cdot S_{100} = \alpha T_{100}

, then

\alpha

is equal to

Show answer

Correct option: A

[JEE Main 2019 · 11 Jan · Shift II]

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