1)sum to n terms
i)1.2^2+2.3^2+3.4^2+........
2)sum to infinity of serirs 3-5r+7r^2-9r^3+.....is 14/9,find r.

Asked by ipaulraj | 3rd Aug, 2014, 10:51: PM

Expert Answer:

1.2 squared plus 2.3 squared plus 3.4 squared plus........  k t h space t e r m space i s space i n space t h e space f o r m space o f space n. open parentheses n plus 1 close parentheses squared rightwards double arrow sum from k equals 1 to n of k. left parenthesis k plus 1 right parenthesis squared equals sum from k equals 1 to n of open square brackets k cubed plus 2 k squared plus k close square brackets equals sum from k equals 1 to n of k cubed plus 2 sum from k equals 1 to n of k squared plus sum from k equals 1 to n of k equals open square brackets fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction close square brackets squared plus 2 open square brackets fraction numerator n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses over denominator 6 end fraction close square brackets plus open square brackets fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction close square brackets equals fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction open square brackets fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction plus fraction numerator 2 n plus 1 over denominator 3 end fraction plus 1 close square brackets equals fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction open square brackets fraction numerator 3 n squared plus 3 n plus 4 n plus 2 plus 6 over denominator 6 end fraction close square brackets equals fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction open square brackets fraction numerator 3 n squared plus 7 n plus 8 over denominator 6 end fraction close square brackets

Answered by Dharma Teja | 4th Aug, 2014, 08:35: AM