Question

find the infinite sum of the series

Answer 1

\(\huge \bf\dfrac{1}{1}+\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+............ \)

Answer 2

\[=\sum_{i=1}^\infty\dfrac{1}{\sum_{k=1}^i k}\\~\\=\sum_{i=1}^\infty\dfrac{2}{i(i+1)}\\~\\=2\sum_{i=1}^\infty\dfrac{1}{i(i+1)}\]

That's how far I can go... :(
Hope this helps?

Answer 3

Wait, I got it... give me min....

Answer 4

what i?

Answer 5

whats i?

Answer 6

u mean 2

Answer 7

Take a look here: http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-convergence-2009-1.pdf

Check page 4.

Answer 8

\[\frac{ 1 }{ i \left( i+1 \right) }=\frac{ 1 }{ i \left( 0+1 \right) }+\frac{ 1 }{ -1\left( i+1 \right) }=\frac{ 1 }{ i }-\frac{ 1 }{ i+1 }\]
\[put ~i=1,2,3,..., \infty ~and~add~vertically~downwards\]
1/1-1/2
1/2-1/3
1/3-1/4
.............0
=1
total sum=2*1=2

Answer 9

thnx very much

Answer 10

yw