help?series?

Question

Answer 1

(6)

Step 1:

The series is .

The series is sum of 4 natural numbers.

The series can be represented in a summation sigma form.

Here the variable represent the starting and ending of the series.

Solution :

.

Answer 2

(7)

Step 1:

The series is .

Rewrite the series .

The series is the sum of squares of first 5 natural numbers.

The series can be represented in a summation sigma form.

Here the variable represent the starting and ending of the series.

Solution :

.

Answer 3

(8)

Step 1:

The series is .

Expand the series.

.

Observe the above sequence, each term is having additional 7 and 8.

It can be rewrite as .

Solution :

.