Sir solve this problem 

Asked by Surjitsp6u | 6th Aug, 2019, 01:04: PM

Expert Answer:

sigma equals 0.9 open parentheses 99 plus 999 plus... plus 9999..9 left parenthesis s t r i n g space u p t o space 101 space d i g i t s right parenthesis close parentheses
equals 0.9 cross times 9 open parentheses 11 plus 111 plus 1111 plus....111...1 left parenthesis s t r i n g space u p t o space 101 space d i g i t s right parenthesis close parentheses
equals 0.9 cross times 9 open parentheses fraction numerator 10 to the power of 100 plus 1 end exponent minus 10 minus 9 cross times 100 over denominator 81 end fraction close parentheses space... space open parentheses S i n c e space 11 plus 111 plus 1111 plus.... u p t o n space t e r m s equals fraction numerator 10 to the power of n plus 1 end exponent minus 10 minus 9 n over denominator 81 end fraction close parentheses
equals 0.9 cross times 9 cross times 10 open parentheses fraction numerator 10 to the power of 100 minus 1 minus 9 cross times 10 over denominator 81 end fraction close parentheses
equals 9 cross times 9 open parentheses fraction numerator 10 to the power of 100 minus 91 over denominator 81 end fraction close parentheses
equals 10 to the power of 100 minus 91
C o m p a r i n g space w i t h space 10 to the power of a minus b comma space w e space h a v e
a equals 100 space a n d space b equals 91
H e n c e comma space a minus b equals 100 minus 91 equals 9

Answered by Renu Varma | 7th Aug, 2019, 10:41: AM

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