left parenthesis 2 to the power of 2001 space end exponent plus space 2 to the power of 1999 right parenthesis divided by left parenthesis space 2 to the power of 2000 space minus space 2 to the power of 1998 right parenthesis  = ?

Asked by Petulla Mishra | 30th Nov, 2014, 09:40: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e x p r e s s i o n fraction numerator open parentheses 2 to the power of 2001 plus 2 to the power of 1999 close parentheses over denominator open parentheses 2 to the power of 2000 minus 2 to the power of 1998 close parentheses end fraction equals fraction numerator 2 to the power of 1999 cross times 2 squared plus 2 to the power of 1999 cross times 1 over denominator 2 to the power of 1998 cross times 2 squared minus 2 to the power of 1998 cross times 1 end fraction space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 2 to the power of 1999 open parentheses 2 squared plus 1 close parentheses over denominator 2 to the power of 1998 open parentheses 2 squared minus 1 close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 2 to the power of 1999 cross times 2 to the power of minus 1998 end exponent open parentheses 2 squared plus 1 close parentheses over denominator open parentheses 2 squared minus 1 close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 2 to the power of 1999 minus 1998 end exponent open parentheses 2 squared plus 1 close parentheses over denominator open parentheses 2 squared minus 1 close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 2 open parentheses 2 squared plus 1 close parentheses over denominator open parentheses 2 squared minus 1 close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 2 open parentheses 4 plus 1 close parentheses over denominator open parentheses 4 minus 1 close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 2 cross times 5 over denominator 3 end fraction space space space space space space space space space space space space space space space space space space space space space space space equals 10 over 3

Answered by Vimala Ramamurthy | 1st Dec, 2014, 08:42: AM