If Sn denotes the sum to n terms of the series 1<=n<=91+22+333+......+999+...... , then for n=>2(9 times)a). Sn-Sn-1=1\\\\9(10n-n2+n) b).Sc). 9(Sn-Sn-1)=n(10n-1) d).S3= 356

Dear swapnil ,

there is a method of solving objective questions called solving by elimination. although we can try about solving for S_n -S_n-1 but in case of objective exams where speed matters it is better to use the former one.

so here , S_n -S_n-1 = a_n  , i.e. nth term.

a) apply n=2 , we get a₂ not equal to 22 so the option is eliminated.

b) not clearly mentioned by you.

c)apply two a2 is 22 but it you shud check also for n =9 where it gives wrong answer so option is eliminated.

d) manually see it is right .

so option d is correct.

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