Question

write an equivalent series with the index of summation beginning at n=1. Show every step please just # 10 and 11 please. Thank you!

Write an equivalent series with the index of summation beginning at n=1. 72041 Show that the function represented by the power series is a solution of the differ 12) = 3 (2+1) >=y=0 13) y = xy' - y = 0

Answer 1

10 put nakal then so akal K-1 50 (k-1)! = s ekal . (k-) Now replace k with n we get: - ht (n-1)!

-~ =0 2n+1 (2n+1)! 2 (k-1)+1 put n - k-1 then K -1=0 (2(k-1)+1)! 2k-2+1 = ? a (QK-2+1)! x (2K-1) (QK-1)! ks!

Now replace k with n , we get in anal (21-1] !