Question

Find the nth term of the given series 2/1 ! + 7/2 ! + 15/3 ! + 26/4 ! + …...

Answer 1

Step-by-step explanation:

Given series 2/1! + 7/2! + 15/3! + 26/4! + …

Here the denominator terms are 1!, 2!, 3!,…

So nth term in denominator = n!

Consider the terms in numerator, 2, 7, 15, 26…an

Here an = 2 + (5 + 8 + 11+…n-1)

= 2 + ((n-1)/2) (10 +(n-2)3) ( since 5,8,11…(n-1) is an AP with a = 5, d = 3 and n = n-1)

= 2 + ((n-1)/2) (10+3n-6)

= [4 + (n-1)(3n+4)]/2

= (4 + 3n2 – 3n + 4n – 4)/2

= (3n2+n)/2

= n(3n+1)/2

So tn = n(3n+1)/2n!