Question

what is the sum of series 0.3+0.33+0.333+....n terms.

Answer 1

HELLO THERE!

If your question is to find out the sum of the above series, then I am giving you the code in Java. You can find it using that code.

Remember first:

0.3 means 3/10, 0.33 means 3/100, etc.
This means that in each iteration, the denominator is multiplied by 10.

Hence, here's your code:

import java.util.*;
class Series
{
public static void main(String args[])
{
Scanner sc = new Scanner (System.in);
int n, i, a = 10; double term = 0.0, sum = 0.0;
System.out.println("Enter the number of terms: ");
n = sc.nextInt();
for (i = 1; i <= n; i++)
{
term = (double) 3/a;
sum = sum + term;
a *= 10;
}
System.out.println("Sum of the series is: " + sum);
}
}

HOPE THIS WILL HELP YOU...

Answer 2

Hi,
What is the sum of the series 0.3+0.33+0.333+…n terms?
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Pradeep Kumar Singh
Pradeep Kumar Singh, B.Tech (M.E.) from Techno India College of Technology (2020)
Answered Aug 31, 2017
0.3+0.33+0.333+……n terms.

First we take 3 as common from the series,

So, 3×{0.1+0.11+0.111+…. n terms}

Now we multiply it by 9 and also divide it by 9 to neutralize the net value

3/9×{0.9+0.99+0.999+…..n terms}

3/9×{(1–0.1)+(1–0.01)+(1–0.001)+……n terms}

1 added upto n times to become ’n' , so we have

3/9×{n -(0.1+0.01+0.001+…… n terms) }

The term we get above (0.1+0.01+0.001+…..n terms) is in GP.

With a=0.1 & R= 0.1 so sum of the series is

Sn= a(1-r^n)/(1-r)

Sn=0.1(1–0.1^n)/(1–0.1)

Sn=(1–0.1^n)/9

So the some of the series is

3/9×{n-1/9(1–0.1^n) }

1/27×{9n-1+0.1^n}

Hope it helps you buddy