if n is odd ,then(1+3+5+7+....to n terms)is equal to.
Full answer with explanation
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if n is odd ,then(1+3+5+7+....to n terms)is equal to.
Full answer with explanation
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We have:
1 + 3 + 5 + 7 + ......... + to n terms
where, n is odd number
We have to find, 1 + 3 + 5 + 7 + ......... + to n terms = ?
Solution:
1 + 3 + 5 + 7 + ......... + to n terms
The given series are in AP.
Here, first term (a) = 1, common difference (d) = 3 - 1 = 2
and number of terms (n) = n
We know that,
The sum of up to n terms
⇒
⇒ (2 + (n - 1)2)
⇒ (2 + 2n - 2)
⇒ (2n)
⇒
∴ 1 + 3 + 5 + 7 + ......... + to n terms =
Thus, 1 + 3 + 5 + 7 + ......... + to n terms =
Given :
n is an odd number .
To Find :
Sum of the series (1+3+5+7+.... to n terms ) = ?
Solution :
∴ It is given that n is an odd number , so the total no of termsin the given series is :
Now , we can see that the given series is an arithmetic progression , where :
First term , a = 1
And common difference , d = 2
∴We know that the formula for the sum of n terms of an AP is given as :
So on using the above formula to find the sum of the given series we get :
So the sum of given series upto n terms is .