1.) Show that the given sequence is eventually strictly increasing or decreasing.
\(\displaystyle \frac {\ n!}{3^n}\limits_{n=1}^\infty\)
an an+1=3n+1( n+1)!∗n! 3n=?
2.) Show: 1∗3 1+2∗4 1+3∗5 1+...=4 3
Telescopic? Sn=k=1∑n(2k−1)(2k+1) 1=2 1k=1∑n(2k−1) 1−k=1∑n2k+1 1=?
Thanks
\(\displaystyle \frac {\ n!}{3^n}\limits_{n=1}^\infty\)
an an+1=3n+1( n+1)!∗n! 3n=?
2.) Show: 1∗3 1+2∗4 1+3∗5 1+...=4 3
Telescopic? Sn=k=1∑n(2k−1)(2k+1) 1=2 1k=1∑n(2k−1) 1−k=1∑n2k+1 1=?
Thanks