The `n^(th)` term of the series `a + a r + a r 2 + − − − −` is

The n^(th) term of the series 6+66+666+.....

Find the n^(th) term of the series 2 + 5 + 10 + 17 + 26 + …

Prove that the sum of n terms of the reciprocals of the terms of the series a, ar, ar^(2),…" is "(1-r^(n))/(a(1-r)r^(n-1))

Find the r^(th) term of the series (2)/(4) + (4)/(4^(2)) + (6)/(4^(3)) + …

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

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