The sum of the series 2/3 + 8/9 + 26/27 + 80/81 + ....... to n terms is
 
a) n - 1/2 ( 3^ -n - 1)
 
b) n - 1/2 (1 - 3^-n)
 
c) n + 1/2( 3^n - 1)
 
d) n - 1/2( 3^n - 1)

Asked by ahuja8087 | 16th Nov, 2015, 04:51: PM

Expert Answer:

begin mathsize 14px style 2 over 3 plus 8 over 9 plus 26 over 27 plus 80 over 81 plus....... u p t o space n space t e r m s equals open parentheses 1 minus 1 third close parentheses plus open parentheses 1 minus 1 over 9 close parentheses plus open parentheses 1 minus 1 over 27 close parentheses plus open parentheses 1 minus 1 over 81 close parentheses plus..... u p t o space n space t e r m s equals n minus open parentheses 1 third plus 1 over 3 squared plus 1 over 3 cubed plus 1 over 3 to the power of 4 plus.....1 over 3 to the power of n close parentheses equals n minus 1 third open parentheses fraction numerator 1 minus open parentheses begin display style 1 third end style close parentheses to the power of n over denominator 1 minus begin display style 1 third end style end fraction close parentheses equals n minus fraction numerator 3 to the power of n minus 1 over denominator 2 cross times 3 to the power of n end fraction equals n minus 1 half open parentheses 1 minus 3 to the power of negative n end exponent close parentheses end style

Answered by Rashmi Khot | 17th Nov, 2015, 09:04: AM