wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

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


A

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

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


Let z = i1+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)2i.e.(in+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, .........


flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Visualising the Terms
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon