Please answer the given question.
Answers
Given summation is
can also be rewritten as
can be further open as
can also be rewritten as
So, it means
Now, we know that
On dividing by (-1), we get
On dividing both sides by x, we get
Now on integrating both sides between the limits x = 0 and x = 1, we get
Now, Consider LHS of above integral
To integrate such integral, we use method of Substitution
So, Substitute
So, above expression can be rewritten as
Using Binomial theorem, we have
Now, Consider RHS of above integral
Hence, From above we concluded that
Answer:
Given summation is
can also be rewritten as
can be further open as
can also be rewritten as
So, it means
Now, we know that
On dividing by (-1), we get
On dividing both sides by x, we get
Now on integrating both sides between the limits x = 0 and x = 1, we get
Now, Consider LHS of above integral
To integrate such integral, we use method of Substitution
So, Substitute
So, above expression can be rewritten as
Using Binomial theorem, we have
Now, Consider RHS of above integral
Hence, From above we concluded that