Sum it-

find the value of summation \sum_{r=0}^{2008}\left [ \frac{2^r}{3} \right ] \\ \\\textup{where [.] is GIF}

2 Answers

106

Asish Mahapatra ·2010-08-17 02:16:05

2^even = 1mod3
2^odd = 2mod3

basically we have
sum = (2⁰-1 + 2²-1 + 2⁴-1 + ... + 2²⁰⁰⁸-1)/3 + (2¹-2 + 2³-2+2⁵-2+...+2²⁰⁰⁷-2)/3

= (2⁰ + 2¹ + 2² + ... + 2²⁰⁰⁸)/3 - (1005 + 2*1004)/3

= (2²⁰⁰⁹-3014)/3

P.S: calc. errors possible

ya rit..thats wat u got to do.

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