JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

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Analyzing +4 | -1

Let

S_n(1 \leq n \leq 9)

denotes the sum of

n

terms of the series

1+22+333+\ldots+\underbrace{999 \ldots 9}_{9 \text { times }}

, then for

2 \leq n \leq 9

View answer and explanation

Correct option: C

9\left(S_n-S_{n-1}\right)=n\left(10^n-1\right)

Option C (

9(S_n-S_{n-1})=n(10^n-1)

) is correct because the difference between consecutive sums simplifies to a geometric series which can be expressed in the given form.

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