Find the value of

rearranging the given expression,
C₀-C₀/2+C₁-C₁/3....

which is (C₀+C₁+C₂....)-(C₀/2+C₁/3+C₂/4...)

the first bracket series upto n terms is 2ⁿ and the second bracket sum can also be found out by writing the binomial expansion of x(1+x)ⁿ,integrating it and putting x=1.

it can easily be done. multipling both sides by x thn integrating, thn dividing both sides by x thn differentiating and putting x=1 in the expansion of (1+x)ⁿ.