sequence Qs

Submitted by asu2008 on Sun, 2008-01-27 00:21

Let Sn be defined as S_n = T₀+ T₁ + T₂ + . . . . . +T_n-1 + T_n, where T_n = (-1)ⁿ⁺¹ (T_n-1 + 1) and T₀ = 1
Find S₁₉₉.
a. -100 b. 100 c. -99 d. -199

Posted on: Wed, 2008-01-30 16:36 #1

Joined: 2007-04-20

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Sn = T0 + T1 + T2 + . . .

S_n = T₀+ T₁ + T₂ + . . . . . +T_n-1 + T_n,

where T_n = (-1)ⁿ⁺¹ (T_n-1 + 1) and T₀ = 1

T₀ = 1

T₁ = 2

T₂ = -3

T₃ = -2

T₄ = 1

Above sequence has a cyclicity of 4 and sum of first 4 terms = -2

So sum of first 200 terms = 50 x (-2)= -100

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Posted on: Fri, 2008-02-01 12:22 #2

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Thanks Nishit for the nice

Thanks Nishit for the nice explanation

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