Interactive practice questions
Consider the infinite sequence $1$1, $x-7$x−7, $\left(x-7\right)^2$(x−7)2, $\left(x-7\right)^3$(x−7)3, $\ldots$…
Complete the gaps to determine for what range of values of $x$x the infinite series has a limiting sum.
$\editable{}<1\andword x-7>\editable{}$<1andx−7>
Solution:
$x<\editable{}\andword x>\editable{}$x<andx>
Medium
2min
Determine the limiting sum of the infinite series $\frac{1}{5}+\frac{3}{5^2}+\frac{1}{5^3}+\frac{3}{5^4}+\frac{1}{5^5}+\text{. . . }$15+352+153+354+155+. . .
Hard
4min
Consider the infinite geometric sequence: $72$72, $-24$−24, $8$8, $-\frac{8}{3}$−83, $\ldots$…
Medium
2min
For a particular geometric sequence, $t_1=7$t1=7 and $S_{\infty}=\frac{35}{4}$S∞=354.
Medium
3min
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