CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The sum to (n+1) terms of the series C02C13+C24C35+ is

A
1n+1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
1n+2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
1n(n+1)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1(n+1)(n+2)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D 1(n+1)(n+2)
Given:
C02C13+C24+(1)nCnn+2

Consider the expansion of
(1x)n=C0C1x+C2x2+(1)n Cnxn

Multiply both sides with x, we get
x(1x)n=C0xC1x2+C2x3+(1)n Cnxn+1

Integrating both sides w.r.t x from 0 to 1,
10x(1x)n dx=10(C0xC1x2+C2x3+(1)n Cnxn+1)dx

[(1x)n+2n+2(1x)n+1n+1]10=[C0x22C1x33+C2x44+(1)n Cnxn+2n+2]10

1(n+1)(n+2)=C02C13+C24+(1)nCnn+2

Hence, option D.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
What is Binomial Expansion?
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon