Sum-the-series-n-C-0-n-C-1-n-C-1-n-C-2-n-C-2-n-C-3-n-C-r-n-C-r-1-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 60416 by Tawa1 last updated on 20/May/19

Sum the series: ^n C_0 ^n C_1 + ^n C_1 ^n C_2 + ^n C_2 ^n C_3 + ... + ^n C_r ^n C_(r + 1)

$$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}:\:\:\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{0}} \overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{1}} \:+\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{1}} \overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{2}} \:+\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{2}} \overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{3}} \:+\:…\:+\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{r}} \overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{r}\:+\:\mathrm{1}} \\ $$

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Sum-the-series-n-C-0-n-C-1-n-C-1-n-C-2-n-C-2-n-C-3-n-C-r-n-C-r-1-

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