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Consider two geometric progressions a1,a...

Consider two geometric progressions `a_1,a_2,a_3,......a_0 & b_1, b_2, b_3,....b_n with a_r=1/b_r=2^(r-1) and an-`other sequence` t_1,t_2,t_3,......t_n`. such that `t_r = cot^-1 (2a_r + b_r)then lim_(n->oo)sum_(r=1)^nt_r` is -

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