how to do summation using syms matlab inbuilt function for below equation

how to use syms matlab summation function for following equation

Answer 1

[Walter Roberson]

syms K
symsum(1/(1+j)^(5*K), K, 0, 3)

[Dr. P. PRAVEEN KUMAR]

thank you so much sir

Answer 2

[Dr. P. PRAVEEN KUMAR]

1.syms k j

or

2.syms k

my dear sir please give explanation for your answer if you select any option from either from 1 or 2

[Walter Roberson]

I would not use either.

Your image uses k (lower-case) with k being multiples of 5. If you were to use k (lower-case) in your symsum then a reader would have a right to expect that your k (lower-case) had the same purpose as the k from the image, namely that it should be restricted to being multiples of 5. Therefore I use a different symbol, K (upper-case) that gets consecutive values, and which the formula transforms to get the needed k.

I would not syms j because in the image, since no information has been given that j might be something else, we can assume that j is the imaginary unit being used in its engineering notation. If j is intended to be something else, then the result of the summation would be quite different.

There are other ways of writing the expression that would use syms k, such as

syms k
sum( subs(1/(1+j)^k, k, [0 5 10 15]) )

or

sum( 1./(1+j).^[0 5 10 15] )