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

Prove by Mathematical Induction, for all nN 12+22+32+.......n2=n(n+1)(2n+1)6

Open in App
Solution

Given,
12+22+32+.......+K2+(K+1)2=(k+1)(k+2)(2k+3)6
Now,
12+22+32+.......+K2+(K+1)2
=k(k+1)(2k+3)6+(k+1)2=k(k+1)(2k+3)+6(k+1)26=(k+1)[k(2k+3)+6(k+1)]6=(k+1)(2k2+7k+6)6=(k+1)(k+2)(2k+3)6

flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Logarithmic Differentiation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon