If S=1/2^2cos1 + 1/cos1¤cos2+1/2^3 cos1 ¤cos2¤cos2^2 + .......... upto 10 terms . If S= sina(cotb-cotc) where a,b,c€N Then find value of a+b+c. where¤ means multipication sign

use brackets or the * symbol to show multiplication.

Secondly lack of brackets to show the order of operation makes an attempt at a solution futile.

pls. do ques . its really a good problem

To find the value of S, we need to substitute each term of the given expression and sum them up. Let's break down the expression and calculate each term step by step.

Given expression: S = 1/2^2cos1 + 1/cos1¤cos2 + 1/2^3cos1¤cos2¤cos2^2 + ...

1. Start with the first term: 1/2^2cos1
- Here, we have 2 raised to the power 2 in the denominator, which means 2 * 2 = 4.
- Also, we have cos(1) in the numerator.
- So, the first term becomes 1/4cos1.

2. Move on to the second term: 1/cos1¤cos2
- Here, we have cos(1)¤cos(2) in the numerator and 1 in the denominator.
- The ¤ symbol represents multiplication, so cos(1)¤cos(2) simply means cos(1) * cos(2).
- So, the second term becomes cos(1) * cos(2).

3. Continue with the third term: 1/2^3cos1¤cos2¤cos2^2
- Similar to the first term, we have 2 raised to the power 3 in the denominator, which means 2 * 2 * 2 = 8.
- We have cos(1)¤cos(2)¤cos(2^2) in the numerator.
- cos(2^2) means cos(4), so the third term becomes 1/8cos(1)¤cos(2)¤cos(4).

Now, we can write the expression S using the calculated terms and sum them up:

S = 1/4cos1 + cos1 * cos2 + 1/8cos1¤cos2¤cos4 + ...

To simplify the expression, let's factor out cos(1) from each term:

S = cos(1)(1/4 + cos2 + 1/8cos(2)¤cos(4) + ...)

Now, we can see that cos(1) is common in each term. So, let's take it out of the sum:

S = cos(1)(1/4 + cos2 + 1/8cos(2)¤cos(4) + ...)
= cos(1)(1/4 + cos2 + 1/8cos(2)¤cos(4) + ... + ...)

Since we are given that S = sin(a)(cot(b) - cot(c)), we can equate the expression with this:

S = sin(a)(cot(b) - cot(c))

Therefore, by comparing the terms, we get:
- cos(1) = sin(a)
- 1/4 + cos2 + 1/8cos(2)¤cos(4) + ... = cot(b) - cot(c)

To find the values of a, b, and c, you need to solve the equations obtained from the comparisons. However, to proceed further and find specific values, we need additional information or data to solve the equations.