© examsiri.com
Question : 3 of 160
Marks:
+1,
-0
Solution:
Since,
n5−5n3+4n=n(n4−5n2+4) =n(n4−4n2−n2+4)=n(n2−1)(n2−4)
=(n−2)(n−1)(n)(n+1)(n+2)=P(n)( let )
For
n=1,2,P(n) is zero so it is divisible by 120 . and for
n=3,P(3)=5l=120 and so on, so the
P(n) is divisible by 120 for all positive integers
n
© examsiri.com
Go to Question: