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Let sn = 1 + q + q2 + …+qn and Tn = 1 +  where q is a real number and q  1. If 101C1+101C2S1+ …… +101C101S100 = T100, then  is equal to

a.

2100

b.

200

c.

299

d.

202


Question ID - 57160 | Toppr Answer

Let sn = 1 + q + q2 + …+qn and Tn = 1 +  where q is a real number and q  1. If 101C1+101C2S1+ …… +101C101S100 = T100, then  is equal to

a.

2100

b.

200

c.

299

d.

202

1 Answer - 5876 Votes

3537

Answer Key : (a) -

101C1+101C2S1+ …… +101C101S100  =  T100

101C1+101C2(1+q) + 101C3(1+q+q2) + … +101C101(1+q+…+q100)

= 2

101C1(1 − q ) +101C2(1 − q2 )+ …. + 101C101(1 − q 101)

= 2

= (2101−1) − ((1+q)101−1)

= 2

⇒ 2101  = 2

 = 2100



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