Question

find the sum of odd integers from 1 to 200​

Answer 1

Answer:

The sum of all the odd numbers from 1 to 200​ is 9950.

Step-by-step explanation:

Answer 2

Answer:

The sum of all the odd numbers from 1 to 200 is 9950.

Step-by-step explanation:

By using the AP we can find the sum of all odd numbers from 1 to 100.

Formula by AP for finding the number of odd numbers present in 1 to200-

T_{n} =a + (n-1)dT

n

=a+(n−1)d --------------------(i)

where,

Number of terms is n

Initial number is a = 1

Difference between number is d = 2

The last number is T_{n}T

n

= 199.

Now, from equation (i) and put the values in it-

T_{n} =a + (n-1)dT

n

=a+(n−1)d

199 = 1 + (n-1)2

199 - 1 = (n-1)2

\dfrac{198}{2} = n-1

2

198

=n−1

99 + 1 = n

n = 100 terms

Now, formula for the sum in AP-

S_{n} =\dfrac{n}{2}(1+(n-1)\times2)S

n

=

2

n

(1+(n−1)×2)

S_{100} =\dfrac{100}{2}(1+(100-1)\times2)S

100

=

2

100

(1+(100−1)×2)

S_{n}S

n

= 50(1 + 198)

S_{n}S

n

= 50×199

S_{n}S

n

= 9950

mark me as brainliest friend