100th term of the series 1+3+7+15+......... is

Answers (1)

Solution:    Let       S=1+3+7+15+.........+T_n     ......(1)

                Again      S=hspace0.4cm1+3+7+........+T_n-1+T_n   .......(2)

                 From  (1)-(2)  we get 

                 Rightarrow          0=[1+2+4+8+.......to hspace0.2cmnhspace0.2cmterms]-T_n

                 Rightarrow                     T_n=1cdot frac2^n-12-1=2^n-1

                  	herefore                   T_100=2^100-1.           

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