Question

4. 100 और 300 के मध्य की सभी विषम संख्याओं का योग ज्ञात कीजिए।
« Find the sum of all the odd integers between 100 and 300.​

Answer 1

Step-by-step explanation:

101+103+105+...........+299= ?

first term= a= 103

last term = 299=L

common difference=d= 2

no. of term=n=?

now,

L=a+(n-1) d

299=101+(n-1)2

by solving..n=100

sum=n/2(a+L) =100/2(101+299)=20000

Answer 2

Answer:

Required sum is 20000.

Step-by-step explanation:

Given numbers are 100 and 300.

We want to find sum of all the odd integers between 100 and 300.

Now, sum of all odd integers between 100 and 300

$t = a + (n - 1)d = 299 \\ 101 + (n - 1) \times 2 = 290 \\ n = 100$

$\frac{n}{2} [2a + (n - 1) \times d] \\= \frac{100}{2} [2\times 101 + (100 - 1) \times 2] \\ = 50 \times 400 \\ = 20000$

Sum of the series is 20000.

Know more about integers:

The integers form a unitary ring, which is most elementary in the following sense: for every unitary ring there is a unique ring homomorphism from the integers to that ring. This universal property of being the initial object in the category of rings characterizes the ring {Z} .

{Z} is not closed under division because the quotient of two integers (eg, 1 divided by 2) need not be an integer. Although natural numbers are closed when exponentiated, integers are not (because the result can be a fraction with a negative exponent).

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