Predict the sum of the entries in row n of Pascal’s triangle.

Question

anonymous · Answer

Does this make sense:

$$\sum Tn= 2 \sum Tn-1$$

anonymous · Answer

What I was trying to get a with that formula was to get the sum of the nth row, you simply multiply the sum of the previous row by 2.

aum · Answer

Is it $$ \sum T_n= 2 \sum T_{n-1} $$

anonymous · Answer

yes, so that makes sense right?

aum · Answer

If the first row is 1, then the sums of subsequent rows will be 2, 4, 8, ....
The sum for the nth row will be  $\large 2^{n-1} $

anonymous · Answer

I get that, so is my method wrong cuz when i try it for myself it works. is the formula i posted the same thing as $$2^{n-1}$$

aum · Answer

Yes, except, the n and (n-1) must be subscripts like I posted in my first reply.

anonymous · Answer

alright thanks

aum · Answer

$\large T_n$ is the sum of the $n^{th}$ row of the Pascal's triangle.

aum · Answer

Then, $T_n = 2*T_{n-1}$.

The sigma is not necessary now because we have already defined $T_n$ as the sum.

anonymous · Answer

so i dont have to put a sigma? just leave it as $$T_{n}=2T _{n-1}$$

anonymous · Answer

oh okay

aum · Answer

correct.

anonymous · Answer

alright thanks :)