find the sum upto n terms 0.3+0.33+0.333+...
Answers
Answer:
Step-by-step explanation:
3[0.1+0.11+0.111....0.111(ntimes)]
39[0.9+0.99+0.999....0.999((ntimes)]
39[(1+1+1...)−(0.1+0.01....)]
39[(n)−1/10(1−1/10n)9/10]
39[(n)−1−1/10n9]
39[9n−1+1/10n9]
9n−1+1/10n27
1.3k Views · View 7 Upvoters
Related QuestionsMore Answers Below
What is sum to n terms of 0.9+0.99+0.999+…?
What will be sum of 0.8+0.88+0.888+0.8888+...n=?
What is the sum of 0+8=?
What is the sum of 0+1?
What is the sum of 0.4+0.44+0.444+0.4444+0.4444?
Ask New Question
Ajinkya Kamath
Ajinkya Kamath, studied at St. Francis Institute of Technology
Answered Aug 31, 2017
Multiply and divide by 3,
The sequence becomes,
1/3(0.9+0.99+0.999+…n)
1/3(1–0.1+1–0.01+1–0.001+…n)
1/3(sum of all ones-(0.1+0.01+0.001…))
1/3(n-0.1(1–0.1^n)/(1–0.1))
1/3(n-1/9(1-0.1^n))
541 Views · View 1 Upvoter
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}
2.4k Views · View 11 Upvoters
Sponsored by MongoDB
Build better apps, faster, with MongoDB Stitch.
Save months of backend coding – focus on the code that matters and getting your app to market faster.
Start now at mongodb.com
Related Questions
What’s is the correct number to 23+55-42+7=?
What is the correct answer for 3+3/3?
What is the answer to 0×0?
What is 8×0+8+8×0+8+8+8+8+8+8×0+8×0=?
What is 0x0+0/0?
Why do we take n/0=not defined, where n is a natural number?
What is a 0+0?
What is the value of 0÷0=?
How much is 1+1+0-0?
What is infinity^0 and 0^infinity? Are they the same?
What is -3+3-3?
What is the value of 0\0?
What is the next number of this sequence 1, 9, 25, 49?
What is the answer for 0÷0×0?
What is 1+3+5+7+9x0?
Ask New Question