Let a+a r1+a r1 2++ooa n da+a r2+a r2 2+...

Let `a+a r_1+a r1 2++ooa n da+a r_2+a r2 2++oo` be two infinite series of positive numbers with the same first term. The sum of the first series is `r_1` and the sum of the second series `r_2dot` Then the value of `(r_1+r_2)` is ________.

Similar Questions

Explore conceptually related problems

Find the sum of the series sum_(r=1)^(n)r xx r!

If the r^(th) term of a series is 1+x+x^(2)+......+x^(r-1), then the sum of the first n terms is

Find the sum of n terms of the series the r^(th) term of which is (2r+1)2^(r).

If r^(th) term of a series is (2r+1)2^(-r) then sum of its infinite terms is

The sum of the series sum_(r=0) ^(n) ""^(2n)C_(r), is

Sum of the series sum_(r=1)^(n) (r^(2)+1)r! is

If the sum of the series sum_(n=0)^(oo)r^(n),|r|<1 is s then find the sum of the series sum_(n=0)^(oo)r^(2n)

Find the sum of firs 100 terms of the series whose general term is given by T_(r)=(r^(2)+1)r! .

The sum of the series sum_(r=0) ^(n) "r."^(2n)C_(r), is