Question

●answer the 3 questions given in the pic ....fast....

●with clear steps ...

●30points !!!

#ch - arithmetic and geometric progressions

Answer 1

18. $2^{51}-52$
      [tex]\Sigma (2^{n}-1) = \Sigma(2^{n})-\Sigma(1) = (2^{n+1}-2)-n = 2^{n+1}-n-2 [/tex]
      Substituting n=50
      $2^{51}-50-2 = 2^{51}-52$
19. $2^{n+1}+n(n+1)-2$
      [tex]\Sigma (2^{n}+2n) = \Sigma(2^{n})+\Sigma(2n) =\Sigma(2^{n})+2\Sigma(n) =(2^{n+1}-2)+2 \frac{n(n+1)}{2} \\ \\ 2^{n+1}+n(n+1)-2[/tex]

20. $\Sigma (x^{n}(x^{n}+y^{n}))=\Sigma(x^{2n}+x^{n}y^{n})=\Sigma(x^{2n})+\Sigma(x^{n}y^{n}) \\ \\= \frac{x^{2}(X^{2n}-1)}{x^{2}-1} +\frac{xy(x^{n}y^{n}-1)}{xy-1}$

Answer 2

Your solution...................