Question

the value of c0/1.3 - c1/2.3 + c2/3.3 - c3/4.3 + ........+(-1)n cn/(n+1).3​

Answer 1

Step-by-step explanation:

Given The value of c0/1.3 - c1/2.3 + c2/3.3 - c3/4.3 + ........+(-1)n cn/(n+1).3

• Now we have  
• So let m = 1/3 (Co/1 – C1/2 + C2/3 – C3/4 +-------------(-1)^n Cn+/ n + 1)
• So (1 – x)^n = Co – C1x + C2x^2 – C3x^3 + C4x^4--------------+ (-1)^n Cnx^n
• So integrating both sides from 0 to 1 we have
•  So - (1 – x)^n+1 / n + 1 ]0 to 1 = C1x – C1 x^2/2 + C2 x^3 / 3 +-----(-1)^n Cn x^n + 1 / n + 1 ]0 to 1
• So 1/n + 1 = Co – C1/2 + C2/3 - ----------------+ (- 1)^nCn / n + 1
•         Substituting we get
•                         1/ 3(n + 1)

Reference link will be

https://brainly.in/question/245120