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Asked by g_archanasharma | 02 Mar, 2019, 19:37: PM
answered-by-expert Expert Answer
begin mathsize 12px style limit as x rightwards arrow infinity of space fraction numerator begin display style sum from k equals 1 to 1000 of end style open parentheses x plus k close parentheses to the power of m over denominator x to the power of m plus 10 to the power of 1000 end fraction space equals space limit as x rightwards arrow infinity of space fraction numerator begin display style x to the power of m space space sum from k equals 1 to 1000 of open parentheses 1 plus k over x close parentheses to the power of m end style over denominator x to the power of m space open parentheses 1 plus begin display style 10 to the power of 1000 over x to the power of m end style close parentheses end fraction space equals space fraction numerator space sum from k equals 1 to 1000 of open parentheses 1 plus 0 close parentheses to the power of m over denominator space open parentheses 1 plus 0 close parentheses end fraction space equals space 1000 end style
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