1thanks
1)
1 + \frac{(1.3) }{6}+ \frac{(1.3.5)}{6.8} +..............
2)\frac{2}{1!} + \frac{6}{2!} + \frac{12}{3!} + \frac{20}{4!} + .................
find the sum
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7 Answers
62kaustab.. i have no idea of where 6 came in the deno from in 1) (I hope prophet or kaymant or bipin sir help us here!)
the second sum is
\\\sum{\frac{r(r+1)}{r!}}=\sum{\frac{r^2-r+2r}{r!}}=\sum{\frac{r(r-1)+2r}{r!}} \\=\sum{\frac{r(r-1)}{r!}}+\sum{\frac{2r}{r!}}
Now try to finish this off from here [1]
1q1
(1-x)^{-\frac{1}{2}}=1+\frac{1}{1!}(\frac{x}{2}) +(\frac{x}{2})^2[ \frac{1.3}{2!}+\frac{1.3.5}{3!}(\frac{x}{2})+........\infty] \\ \\ \int_{0}^{1}{\frac{dx}{\sqrt{1-x}}}=1+\frac{1}{2.2!}+\frac{1}{2^2}(S-1) \\ \\ \\ \boxed{S=4}
