You visited us 3 times! Enjoying our articles? Unlock Full Access!

Convexity

Let S n =[ n;...

Question

Let $S_{n} = (_{0}^{n}) - (_{1}^{n - 1}) + (_{2}^{n - 2}) - \dots$
Note that the series does terminate. Recall that $^{p} C_{q} = 0$ if $p < q$
$S_{2010}$ equals

-1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 1
$S_{n} = S_{n + 1} \forall n$
$S_{1} = 1, S_{2} = 0, S_{3} = - 1, S_{4} = - 1, S_{5} = 0, S_{6} = 1$

Suggest Corrections

Similar questions

S_{n} = (_{0}^{n}) - (_{1}^{n - 1}) + (_{2}^{n - 2}) - \dots

^{p} C_{q} = 0

p < q

S_{n}

S_{n} = (_{0}^{n}) - (_{1}^{n - 1}) + (_{2}^{n - 2}) - \dots

^{p} C_{q} = 0

p < q

S_{2009}

S_{n} = (\frac{n}{1}) sin a + (\frac{n}{2}) sin 2 a + \dots + (\frac{n}{n}) sin n a

T_{n} = (\frac{n}{1}) cos a + (\frac{n}{2}) cos 2 a + \dots + (\frac{n}{n}) cos n a

n \in N

a

a \neq (2 n - 1) \frac{π}{2}

(Here, (\frac{n}{r}) =^{n} C_{r})

(x_{0}, y_{0})

(2 x)^{l n 2} = (3 y)^{l n 3}

3^{l n x} = 2^{l n y}

x_{0}

A B C D

Join BYJU'S Learning Program