- #1
jonroberts74
- 189
- 0
Homework Statement
prove by induction [tex]\sum_{j=1}^{n+1} j \cdot 2^j = n \cdot 2^{n+2}+2; n \ge 0[/tex]2. The attempt at a solution
P(0)
[tex]\sum_{j=1}^{0+1} j \cdot 2^j = 0 \cdot 2^{0+2}+2[/tex]
[tex] 2+2 [/tex]
here is where I need some help
is P(k)
[tex]\sum_{j=1}^{k+1} j \cdot 2^j = (k+1) \cdot 2^{k+3}+2[/tex] ??
then
P(k+1) [tex]\sum_{j=1}^{k+2} j \cdot 2^j = (k+2)\cdot 2^{k+4}+2[/tex]
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