Prove that the series a+ar+ar²+..... Which is a series in GP is convergent only when common ratio r<1
If k is a funite number and ∑ uⁿ Converse to a sum s then ∑ kuⁿ also Converse and its sum is ks also if the first series diverse or oscilates so does the second unless k=0
if the series u¹+u²+u³.....and v¹+v²+v³+... convert and their sums are s and t respectively then
- u¹+u²+u³+........ Converse and its sum is s.
- v¹+v²+v³+........ Diverges and its sum is t.
if the series u¹+u²+u³.....and v¹+v²+v³+... convert and their sums are s and t respectively then
- u¹+u²+u³+........ Converse and its sum is s.
- v¹+v²+v³+........ Diverges and its sum is t.
if the series u¹+u²+u³.....and v¹+v²+v³+... convert and their sums are s and t respectively then
- u¹+u²+u³+........ Converse and its sum is s.
- v¹+v²+v³+........ Diverges and its sum is t.
if the series u¹+u²+u³.....and v¹+v²+v³+... convert and their sums are s and t respectively then
- u¹+u²+u³+........ Converse and its sum is s.
- v¹+v²+v³+........ Diverges and its sum is t.
if the series u¹+u²+u³.....and v¹+v²+v³+... convert and their sums are s and t respectively then
- u¹+u²+u³+........ Converse and its sum is s.
- v¹+v²+v³+........ Diverges and its sum is t.
if the series u¹+u²+u³.....and v¹+v²+v³+... convert and their sums are s and t respectively then
- u¹+u²+u³+........ Converse and its sum is s.
- v¹+v²+v³+........ Diverges and its sum is t.