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# Consecutive terms of a series, B. Stat Hons., 2003 Problem-1

The simplest example from sequence and series of comparing two consecutive terms of the sequnce. Learn in this self-learning module for math olympiad

## Comparing consecutive terms of a series

The question is based upon sequence and finding the relation between consecutive terms of a series with its next or previous term if the expression of its nth term is given.

## Try the problem

Let $a_n = \frac{{10^{n+1}+1}}{10^n +1}$, for $n=1,2,3……$ . Then

(A) for every $n, a_n \geq a_{n+1} ;$

(B) for every $n, a_n \leq a_{n+1} ;$

(C) there is an integer k such that $a_{n+k}=a_n$ for all n.

(D) None of the above.

I.S.I. Entrance B. stat. 2003, Objective, Problem 1

Sequence and series

6 out of 10

Secrets in mathematics.

## Use some hints

we can put value of n , as it is equal to list of given natural numbers. n=1,2,3,4,……… and verify the result with the option.

We can see weather the series is converging or diverging to a value, means is there any pattern of the next term with the previous term in the sense of ratio of the two terms.

Also to generalize everything we can put n+1 in place of n in the expression $a_n = \frac{{10^{n+1}+1}}{10^n +1}$ and then we can divide the $a_{n+1}$ by $a_{n}$ to get the required comparison ratio.

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