the sum of the series 1+3+5+7+......2n-1
Answers
There are n terms in the series . Because last odd term =2n-1 and rth odd term is denoted by 2r-1 .
We can also calculate number of terms by formula.
Let there are r terms in the series .
ar = a + (r-1)d
ar = rth term =2n-1
a=first term =1
d=common difference =2
2n-1 =1+ 2(r-1)
2n-1=1+2r -2
2n=2r
r=n
so number of terms =n
The sum of n terms of series
=n/2 [2a + (n-1)d]
=n/2 [2(1) +2(n-1)]
=n/2 [2n]
=n²
There are n terms in the series . Because last odd term =2n-1 and rth odd term is denoted by 2r-1 .
We can also calculate number of terms by formula.
Let there are r terms in the series .
ar = a + (r-1)d
ar = rth term =2n-1
a=first term =1
d=common difference =2
2n-1 =1+ 2(r-1)
2n-1=1+2r -2
2n=2r
r=n
so number of terms =n
The sum of n terms of series
=n/2 [2a + (n-1)d]
=n/2 [2(1) +2(n-1)]
=n/2 [2n]
=n²