Here's the question you clicked on:
nissn
how to find the sum of this?
\[\sum_{k=1}^{\infty}\left( 2^{-k}+5^{-k+1} \right)\]
break in to two parts and add
first one is \[\sum_{k=1}^{\infty}\frac{1}{2^k}=1\]
how did you find that? (Haven't done this in a long time)
the sum is 9/4 (after wolframalpha) but I don't know how to find it
the first term is a geometric series with first term 1/2 and ratio 1/2, the second term is a geometric series with first term 1 and ratio 1/5 use the formula \[S=\frac{ a_1 }{ 1-r }\] to find the sum of an infinite geometric series
so then it is s =0.5/(1-0.5)=1 and 1/(1-1/5)=5/4 1+5/4 =9/4