The value of expression -132-1-152-1-172-1-192-1-1452-1- is

nbsp;[13^2 1]+[15^2 1]+[17^2 1]+[19^2 1]+.....[145^2 1] is also written as ⇒[18+124+ 148+ 180+ ......12024+ nbsp; ] ⇒12[28+224+ 248+ 280+ ......22024+ ...

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Standard VIII

Mathematics

Algebraic Identities

The value of ...

Question

The value of expression $[\frac{1}{3^{2} - 1}] + [\frac{1}{5^{2} - 1}] + [\frac{1}{7^{2} - 1}] + [\frac{1}{9^{2} - 1}] + . . . . . [\frac{1}{45^{2} - 1}]$ is

\frac{13}{45}

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\frac{1}{2}

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\frac{11}{46}

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\frac{1}{4}

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Solution

The correct option is C $\frac{11}{46}$
$[\frac{1}{3^{2} - 1}] + [\frac{1}{5^{2} - 1}] + [\frac{1}{7^{2} - 1}] + [\frac{1}{9^{2} - 1}] + . . . . . [\frac{1}{45^{2} - 1}]$ is also written as

$\Rightarrow [\frac{1}{8} + \frac{1}{24} + \frac{1}{48} + \frac{1}{80} + . . . . . . \frac{1}{2024} +]$

$\Rightarrow \frac{1}{2} [\frac{2}{8} + \frac{2}{24} + \frac{2}{48} + \frac{2}{80} + . . . . . . \frac{2}{2024} +]$

$\Rightarrow \frac{1}{2} [(\frac{1}{2} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{6}) + (\frac{1}{6} - \frac{1}{8}) + (\frac{1}{8} - \frac{1}{10}) + . . . . . . + + (\frac{1}{44} - \frac{1}{46})]$

$\Rightarrow \frac{1}{2} [\frac{1}{2} - \frac{1}{46}]$

$\Rightarrow \frac{1}{2} [\frac{44}{2 \times 46}]$

$\Rightarrow \frac{11}{46}$

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Similar questions

Q. Observe the following pattern

1^{2} = \frac{1}{6} [1 \times (1 + 1) \times (2 \times 1 + 1)] 1^{2} + 2^{2} = \frac{1}{6} [2 \times (2 + 1) \times (2 \times 2 + 1)] 1^{2} + 2^{2} + 3^{2} = \frac{1}{6} [3 \times (3 + 1) \times (2 \times 3 + 1)] 1^{2} + 2^{2} + 3^{2} + 4^{2} = \frac{1}{6} [4 \times (4 + 1) \times (2 \times 4 + 1)]

and find the values of each of the following:
(i) 1² + 2² + 3² + 4²+ ... + 10²
(ii) 5² + 6² + 7² + 8² + 9² + 10² + 11² + 12²

\frac{1}{3^{2} - 1} + \frac{1}{5^{2} - 1} + \frac{1}{7^{2} - 1} + . . . . . . + \frac{1}{35^{2} - 1} =

Q. If

S = \frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + \frac{1}{4^{2}} + . . . . . . . . . . . . .

\infty

then find

\frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} + \frac{1}{7^{2}} + . . . . . . . . . . . . .

\infty

in terms of S.

Q. If

\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . . u p t o \infty = \frac{π^{2}}{6}

, then value of

\frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} + . . . . . u p t o \infty

is-

Q. If

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

upto

\infty = \frac{π^{2}}{6}

, then value of

\frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} + . . . . . .

upto

\infty

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The value of expression [132−1]+[152−1]+[172−1]+[192−1]+.....[1452−1] is

The correct option is C 1146 [132−1]+[152−1]+[172−1]+[192−1]+.....[1452−1] is also written as ⇒[18+124+148+180+......12024+] ⇒12[28+224+248+280+......22024+] ⇒12[(12−14)+(14−16)+(16−18)+(18−110)+......++(144−146)] ⇒12[12−146] ⇒12[442×46] ⇒1146

The value of expression $[\frac{1}{3^{2} - 1}] + [\frac{1}{5^{2} - 1}] + [\frac{1}{7^{2} - 1}] + [\frac{1}{9^{2} - 1}] + . . . . . [\frac{1}{45^{2} - 1}]$ is