Question

period of cos(x+2x+3x+........+nx)is​

Answer 1

Given: The trigonometric term cos(x+2x+3x+........+nx)

To find: Period of the given term.

Solution:

• Now we have given the term:

               f(x) = cos(x+2x+3x+........+nx)                                  

• Now we know that ∑ r = n(n+1)/2      (∑ from r = 0 to r = n)

• We can rewrite it as:

               cos(n(n+1)/2 × x)  

               cos(xn(n+1)/2)  

• Now we know that the period of cos x is 2π.

• Then period of f(x) will be:

               2π x (2/n(n+1))

Answer:

               So the period of given term is: 4π//n(n+1)

Answer 2

Here is your answer

I HOPE YOU UNDERSTAND AND IT'S HELPFUL TO YOU.