Let E -1-12-1-22-1-32- - then-A- E 3-2C- E -2D- E -2

The correct options are A E lt;3 B E gt;32 D E lt;2E=11^2+12^2+13^2+.... 12.2 lt;11.2;13.3 lt;12.3 E lt;1+11.2+12.3+... =1+2 11.2+3 22.3+4 33.4+... ...

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Byju's Answer

Standard XII

Mathematics

Sequence

Let E =1/12+1...

Question

Let $E = \frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . .$ then,

E < 3

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E > \frac{3}{2}

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E > 2

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E < 2

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Solution

The correct options are
A $E < 3$
B $E > \frac{3}{2}$
D $E < 2$
$E = \frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . .$
$\frac{1}{2.2} < \frac{1}{1.2}; \frac{1}{3.3} < \frac{1}{2.3}$
$E < 1 + \frac{1}{1.2} + \frac{1}{2.3} + . . .$
$= 1 + \frac{2 - 1}{1.2} + \frac{3 - 2}{2.3} + \frac{4 - 3}{3.4} + . . .$
$E < 1 + 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} . . . .$
$E < 2$
$E < 3$
$E = \frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . .$
$E > 1 + \frac{3 - 2}{2.3} + \frac{4 - 3}{3.4} + . . . .$
$E > 1 + \frac{1}{2}$
$E > \frac{3}{2}$

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Similar questions

Q. Let

E = \frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . .

then,

Q. If

a, b, c

are cube roots of unity, then

∣ ∣ ∣ ∣ ∣ \begin{matrix} e^{a} & e^{2 a} & e^{3 a} - 1 e^{b} & e^{2 b} & e^{3 b} - 1 e^{c} & e^{2 c} & e^{3 c} - 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

is equal to

Q. If

1 \int 0 \frac{e^{t}}{1 + t} d t = a,

then

1 \int 0 \frac{e^{t}}{(1 + t)^{2}}

is equal to

Q. Consider the following process

Δ

H (k J / m o l)

\frac{1}{2}

A \to B

+ 150

3 B

⟶

2 C + D

- 125

E + A

⟶

2 D

+ 350

For;

B + D

⟶

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will be :

Q. Consider the following processes.

	$Δ H (k J / m o l)$
$1 / 2 A \to B$	+150
$3 B \to 2 C + D$	-125
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For

B + D \to E + 2 C, Δ H

will be:

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Let E=112+122+132+.... then,

The correct options are A E<3 B E>32 D E<2E=112+122+132+.... 12.2<11.2;13.3<12.3 E<1+11.2+12.3+... =1+2−11.2+3−22.3+4−33.4+... E<1+1−12+12−13+13−14.... E<2 E<3 E=112+122+132+.... E>1+3−22.3+4−33.4+.... E>1+12 E>32

Let $E = \frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . .$ then,