Question

Show that
1/1.3 + 1/3.5 + 1/5.7 + ... = 3/2
help please :)

Answer 1

What d o u want ?:)

Answer 2

how to show that?

Answer 3

we have :
1/31/10+1/57/10+...=3/2
10/31+10/57+...=3/2
k ?

Answer 4

how do u get 1/31/10 ?

Answer 5

\[ \sum_{n=0}^\infty \frac{1}{(2n + 1)(2n + 3)} \]
hint: do partial fractions and use telescoping.

Answer 6

ok thanks :)

Answer 7

if that helps you, then try showing your working here. perhaps it would help someone.

Answer 8

\[\frac{ 1 }{ 1.3 }+\frac{ 1 }{ 3.5 }+\frac{ 1 }{5.7 }+....\]
1,3,5,........
it is an A.P sequence with a=1, d=3-1=2
tn=a+(n-1) d=1+(n-1)2=1+2n-2=2n-1
second term is 2 more.i.e.,2n-1+2=2n+1
\[tn=\frac{ 1 }{\left( 2n-1 \right)\left( 2n+1 \right) }=\frac{ 1 }{\left( 2n-1 \right)\left( 1+1 \right) }+\frac{ 1}{\left( -1-1 \right)\left( 2n+1 \right) }\]
\[=\frac{ 1 }{ 2 }\frac{ 1 }{2n-1 }-\frac{ 1 }{ 2 }\frac{ 1 }{ 2n+1 }\]
you can solve further.