Ask
your own question, for FREE!
Mathematics
13 Online
\[\Huge{1^2+2^2+3^2...........n^2=???}\]
Still Need Help?
Join the QuestionCove community and study together with friends!
@waterineyes @UnkleRhaukus Plz help
\[\Huge{Ans.{n(n+1)(2n+1)\over6}}\]
Square pyramidal number
sorry \[\large (k+1)^3-k^3=3k^2+3k+1\] take sigma k=1 to n from both sides
Still Need Help?
Join the QuestionCove community and study together with friends!
(k+1)^3=k^3+3k^2+3k+1 and we will havve (k+1)^3-k^3=3k^2+3k+1 a telescopic sum...(n+1)^3-0=3*\[\sum_{0}^{n}k^2\]+3*\[\sum_{0}^{n}k\]+\[\sum_{0}^{n}1\]
and as we know...\[\sum_{0}^{n}k=n(n+1)/2 and \sum_{0}^{n}1=n+1 \] you can finish it by yourself :)
no i want full sol @Neemo
\[okk (n+1)^3=3\sum_{0}^{n}k^2+3n(n+1)/2+n-1\] then \[3\sum_{0}^{n}k^2=(n+1)((n+1)^2-3n/2 -1)\] \[6\sum_{0}^{n}k^2=(n+1)(2n^2+4n+2-3n-2)\] \[6\sum_{0}^{n}k^2=(n+1)n(2n+1)\]
in the third line i multiplied both side by 2 ! It's clear now ?!
Can't find your answer?
Make a FREE account and ask your own questions, OR help others and earn volunteer hours!
Join our real-time social learning platform and learn together with your friends!
Join our real-time social learning platform and learn together with your friends!
Latest Questions
Countless7Echos:
Ah trying out the whole T.V girl drawing :p (I love drawing eyes)
SnowyBreaks:
You ever get the types of dreams where it feels as if you aren't breathing? And w
laylasnii13:
Poem/diary i wrote I Want Out Iu2019m so tired of screaming into walls. Every fight with my mom leaves something broken and itu2019s not just plates or slam
Countless7Echos:
Aye.. I need actually some help on the shading here.. if the light is from above too I just feel something is off.
2 hours ago
7 Replies
5 Medals
14 hours ago
6 Replies
0 Medals
1 day ago
13 Replies
3 Medals
3 days ago
19 Replies
3 Medals