Help with any of them is greatly appreciated

7 + 14 + 28 + · · · is Sn = 7(2n − 1).
Prove that the nth partial sum is always 7 less than the (n + 1)th term

The sequence Tn = 2n+3+2^n is the sum of an AP and a GP. Use a combination of
AP and GP formulae to find Sn

Suppose that Tn = arn−1 is a GP with a limiting sum.
(a) Find the common ratio r if the limiting sum equals 5 times the first term

Consider the series 1 + 2/2 + 3/4 + 4/8+ 5/16 + 6/32 + · · ·.
(a) Write out the terms of Sn and 2Sn .
(b) Subtract to get an expression for Sn .
(c) Find the limit as n→∞, and hence find S∞.