If sn-r-0n1-ncr and tn-r-0nr-nCr- then tn-sn-

The correct option is B t_n=∑ ^n_r=0r/^nC_r=∑ ^n_r=0n r/^nC_n r=∑ ^n_r=0n r/^nC_r=n∑ ^n_r=01/^nC_r ∑ ^n_r=0r/^nC_r=ns_n t_n ⇒ 2t_n=ns_n⇒t_n/s_n=n/2 ...

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Byju's Answer

Standard XII

Mathematics

Greatest Binomial Coefficients

If sn=∑r=0n1/...

Question

$I f s_{n} = \sum_{r = 0}^{n} \frac{1}{n_{C_{r}}} a n d t_{n} = \sum_{r = 0}^{n} \frac{r}{n_{C_{r}}}, t h e n \frac{t_{n}}{s_{n}} =$

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n -1

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Solution

The correct option is A
$t_{n} = \sum_{r = 0}^{n} \frac{r}{^{n} C_{r}} = \sum_{r = 0}^{n} \frac{n - r}{^{n} C_{n - r}} = \sum_{r = 0}^{n} \frac{n - r}{^{n} C_{r}} = n \sum_{r = 0}^{n} \frac{1}{^{n} C_{r}} - \sum_{r = 0}^{n} \frac{r}{^{n} C_{r}} = n s_{n} - t_{n} \Rightarrow 2 t_{n} = n s_{n} \Rightarrow \frac{t_{n}}{s_{n}} = \frac{n}{2}$

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Similar questions

Q. IF

S_{n} = \sum_{r = 0}^{n} \frac{1}{^{n} C_{r}}

and

t_{n} = \sum_{r = 0}^{n} \frac{r}{^{n} C_{r}},

then

\frac{t_{n}}{S_{n}}

is equal to

Q. If

S_{n} = \sum_{r = 0}^{n} \frac{1}{^{n} C_{r}}

and

t_{n} = \sum_{r = 0}^{n} \frac{r}{^{n} C_{r}}

then

\frac{t_{n}}{S_{n}}

is equal to

Q. If

s_{n} = n \sum r = 0 \frac{1}{^{n} C_{r}}

and

t_{n} = n \sum r = 0 \frac{r}{^{n} C_{r}},

then

\frac{t_{n}}{s_{n}}

is equal to -

Q. If

S_{n} = n \sum r = 0 \frac{1}{^{n} C_{r}}

and

P_{n} = n \sum r = 0 \frac{r}{^{n} C_{r}}

then

\frac{S_{n}}{P_{n}}

Q. If

S_{n} = n \sum r = 0 \frac{1}{^{n} C_{r}}

and

t_{n} = n \sum r = 0 \frac{r}{^{n} C_{r}}

, then

\frac{t_{n}}{s_{n}} =

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If sn=∑nr=01nCr and tn=∑nr=0rnCr,thentnsn=

The correct option is A tn=∑nr=0rnCr=∑nr=0n−rnCn−r=∑nr=0n−rnCr=n∑nr=01nCr−∑nr=0rnCr=nsn−tn⇒2tn=nsn⇒tnsn=n2

$I f s_{n} = \sum_{r = 0}^{n} \frac{1}{n_{C_{r}}} a n d t_{n} = \sum_{r = 0}^{n} \frac{r}{n_{C_{r}}}, t h e n \frac{t_{n}}{s_{n}} =$