Question

what is the tens digit in the sum of the series 1+11+111+...50 terms?​

Answer 1

Answer:

Step-by-step explanation:

Well in the given case the sum can be easily found out, but imagine if there were some terms like the sum of

1+11+111+1111+……………n terms

where n is a large number. Finding out the actual sum wouldn’t be feasible in such cases!

So, I’ll be deriving a technique here to find the sum of such series with n terms, and will be finding out the required sum using it.

Let,

=1+11+111+1111+……….

9=9+99+999+9999+..........

9=(10−1)+(100−1)+(1000−1)........

9=10+100+1000+10000+......−

The above terms form a GP with,

a=10 and common ratio(r)=10

SO,

9=10(10−1)10−1−

=19∗(10(10−1)9−)

Checking the formula for the question we’ve n=5.

S=12345.

So we can very well see that our method works.