Question

1. 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) =

Answer 1

@mayankdevnani

Answer 2

\[t _{n}=4n \left( 4n+2 \right)=16n^2+8n\]
\[\Sigma~t _{n}=16 ~\Sigma n^2+8 ~\Sigma n\]

Answer 3

do you know \[\Sigma n^2 ~and~\Sigma ~n\]?

Answer 4

\[\Sigma n^2=?\]

Answer 5

No. The lesson for this confused me entirely.

Answer 6

\[\Sigma~n=?\]

Answer 7

Isn't that like the summation notation of n?

Answer 8

\[\Sigma~n^2=\frac{ n \left( n+1 \right)\left( 2n+1 \right) }{ 6 }\]
\[\Sigma n=\frac{ n \left( n+1 \right) }{ 2 }\]

Answer 9

apply these and simplify if possible.

Answer 10

can you show me your work?

Answer 11

I haven't done any work. I don't know anything about this, so I don't know what I'm doing.

Answer 12

o kay i will solve.

Answer 13

I would like to understand how to do it tho.

Answer 14

\[\sum t _{n}=16\frac{ n \left( n+1 \right)\left( 2n+1 \right) }{ 6 }+8\frac{ n \left( n+1 \right) }{ 2 }\]

Answer 15

\[=8\frac{ n \left( n+1 \right) }{ 2 }\left[ \frac{ 2 }{ 3 } \left( 2n+1 \right)+1\right]\]
\[=4n(n+1)\left[ \frac{ 4n+2+3 }{ 3 } \right]=\frac{ 1 }{ 3 }4n \left( n+1 \right)\left( 4n+5 \right)\]

Answer 16

I don't really understand.

Answer 17

@sleepyjess could you explain this?

Answer 18

can you tell me where you have problem?

Answer 19

i don't understand how you got this

Answer 20

(x+1)^2=x^2+2x+1
(x+1)^2-x^2=2x+1
put x=1,2,3,...,n

Answer 21

Thanks I think I kind of understand now.