Question

Find first partial sums S1 S2 S3 S4 and suggest a formula for Sn
\[\frac{ 1 }{ 1*2 }+\frac{ 1 }{ 2*3 }+\frac{ 1 }{ 3*4 }+...+ \frac{ 1 }{ n(n+1) }+...\]

Answer 1

you welcome

Answer 2

The sum is,
\[\frac{1}{n(n+1)}\]
So the first term, you would simply plug 1 into it as "n".

Answer 3

i suggest you actually add and see what you get as a partial sum

Answer 4

Well, it asks for S1-4... So you would need to solve out for those... right?

Answer 5

\[S_1=\frac{1}{2}\]
\[S_2=\frac{1}{2}+\frac{1}{6}=\frac{2}{3}\]

Answer 6

I will leave this to you, you seem like you have it well in hand.

Answer 7

Wait, so i add them together?

Answer 8

For S2 you take what you got for n=1 and n=2, and add them together, yes.

Answer 9

how do i find S4?

Answer 10

Well,
S1 is n=1
S2 is n=1+n=2
S3 is n=2+n=3
S4 is n=3+n=4
Does this make sense?

Answer 11

Why does n=1?

Answer 12

I assume this is what you are doing?
\[\sum_{1}^{\infty} \frac{1}{n(n+1)}\]

Answer 13

Oh! I get it! Thank you! :)