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

Find the sum of n terms of the following series:
4-1n+4-2n+4-3n+... [CBSE 2017]

Open in App
Solution

Let the given series be X = 4-1n+4-2n+4-3n+...
=4+4+4+...-1n+2n+3n+...=41+1+1+...-1n1+2+3+...=S1-S2
S1=41+1+1+...a=1, d=0S1=4×n22×1+n-1×0 Sn=n22a+n-1dS1=4n
S2=1n1+2+3+...a=1, d=2-1=1S2=1n×n22×1+n-1×1=122+n-1=121+n
Thus, S=S1-S2=4n-121+nS=8n-1-n2=7n-12
Hence, the sum of n terms of the series is 7n-12.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometric Progression
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon