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Question

The value of i1+3+5+......+(2n+1) is


A

i if n is even, - i if n is odd

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B

1 if n is even, - 1 if n is odd

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C

1 if n is odd, i if n is even

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D

i if n is even, - 1 if n is odd

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Solution

The correct option is C

1 if n is odd, i if n is even


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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