Question
The value of i1+3+5+......+(2n+1) is
Answer: Option C
:
C
Let z =i[1+3+5+......+(2n+1)]
Clearly series is A.P with common difference = 2
∵Tn = 2n-1 And Tn+1 = 2n+1
So, number of terms in A.P. = n+1
Now, sn+1=n+12 [2.1+(n+1-1)2]
⇒ Sn+1=n+12[2+2n]=(n+1)2 i.e., i(n+1)2
Now put n = 1,2,3,4,5,........
n = 1, z =i4 = 1, n = 2, z = i5= -1 ,
n = 3, z =i8 = 1, n = 4, z = i10= -1 ,
n = 5, z =i12 = 1, .........
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:
C
Let z =i[1+3+5+......+(2n+1)]
Clearly series is A.P with common difference = 2
∵Tn = 2n-1 And Tn+1 = 2n+1
So, number of terms in A.P. = n+1
Now, sn+1=n+12 [2.1+(n+1-1)2]
⇒ Sn+1=n+12[2+2n]=(n+1)2 i.e., i(n+1)2
Now put n = 1,2,3,4,5,........
n = 1, z =i4 = 1, n = 2, z = i5= -1 ,
n = 3, z =i8 = 1, n = 4, z = i10= -1 ,
n = 5, z =i12 = 1, .........
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