Question

500 और 1,000 के बीच प्राकृतिक संख्याओं का योग ज्ञात कीजिए जो 13 से विभाजित हो जाती है।
Find the sum of all natural numbers between 500 and 1,000 which are divisible by 13.​

Answer 1

Answer:

47,840

Step-by-step explanation:

13×39=507

So the series which are exactly divisible by 13....

(13×39=507),520,533,..........(76x13=988)

76-12=64..

Sn=64/2(507+988)

=64/2(1495)

=64×747.5

=47,840

Answer 2

Answer:

The sum of natural number between 500 to 1000 that are divisible by 13 is S_{38} =18772

Step-by-step explanation:

Here required is the sum of all the natural numbers between 500 and 1000 which are divisible by 13.

The very next natural number after 500 that is divisible by 13 is 13×39=507

So the series which are exactly divisible by 13 starts from a=507

The nearest natural number divisible by 13 before 100 is 76x13=988

So the series which are exactly divisible by 13 ends with$a_{n}=988$

The series is as below:

520,533,..........988

and the difference in each term is d=13

formula for nth term is $a_{n}=a+(n-1)d\\988=507+(n-1)13\\481=(n-1)13\\\frac{481}{13} =n-\\\frac{494}{13} =n\\n=38$

Therefore 988 is 38th term in series and the sum of thus series upto 38th term is as below:

$S_{n}=\frac{n}{2} (a+(n-1)d)$

$S_{38} =\frac{38}{2} (507+(38-1)13)\\S_{38}=19 (507+(37)13)\\S_{38}=19 (507+481)\\S_{38}=19 (988)\\S_{38}=18772$

So the sum of natural number between 500 to 1000 that are divisible by 13 is S_{38} =18772