Math, asked by kiara1231843, 9 months ago

Answer it...
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Answers

Answered by Anonymous
2

Step-by-step explanation:

hey mate

please refer to the attached pictures for detailed solution.

i have first transformed the expression to suit my purpose.often,we require to set the expression in difference form to solve the sum of the series.after finding the sum of the series i have just evaluated the inverse function.

please ask your queries in you have any in understanding it.

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Answered by kiara9514
1
&lt;!DOCTYPE html&gt;<br /><br />&lt;html lang="en"&gt;<br /><br />&lt;head&gt;<br /><br />&lt;title&gt;Bulb&lt;/title&gt;<br /><br />&lt;/head&gt;<br /><br />&lt;body&gt;<br /><br />&lt;main&gt;<br /><br />&lt;input class="l" type="checkbox"&gt;<br /><br />&lt;/main&gt;<br /><br />&lt;style&gt;<br /><br />*, *:before, *:after {<br /><br />box-sizing: border-box;<br /><br />margin: 0;<br /><br />padding: 0;<br /><br />}<br /><br />:root {<br /><br />/* minFontSize + (maxFontSize - minFontSize) * (100vw - minVWidth)/(maxVWidth - minVWidth) */<br /><br />font-size: calc(64px + (80 - 64) * (100vw - 320px)/(960 - 320));<br /><br />}<br /><br />body, input {<br /><br />font-size: 1em;<br /><br />line-height: 1.5;<br /><br />}<br /><br />body {<br /><br />background: #bbb;<br /><br />}<br /><br />input {<br /><br />display: block;<br /><br />margin-bottom: 1.5em;<br /><br />}<br /><br />main {<br /><br />padding: 1.5em 0 0 0;<br /><br />text-align: center;<br /><br />}<br /><br />.l {<br /><br />background-color: rgba(0,0,0,0.7);<br /><br />border-radius: 0.75em;<br /><br />box-shadow: 0.125em 0.125em 0 0.125em rgba(0,0,0,0.3) inset;<br /><br />color: #fdea7b;<br /><br />display: inline-flex;<br /><br />align-items: center;<br /><br />margin: auto;<br /><br />padding: 0.15em;<br /><br />width: 3em;<br /><br />height: 1.5em;<br /><br />transition: background-color 0.1s 0.3s ease-out, box-shadow 0.1s 0.3s ease-out;<br /><br />-webkit-appearance: none;<br /><br />-moz-appearance: none;<br /><br />appearance: none;<br /><br />}<br /><br />.l:before, .l:after {<br /><br />content: "";<br /><br />display: block;<br /><br />}<br /><br />.l:before {<br /><br />background-color: #d7d7d7;<br /><br />border-radius: 50%;<br /><br />width: 1.2em;<br /><br />height: 1.2em;<br /><br />transition: background-color 0.1s 0.3s ease-out, transform 0.3s ease-out;<br /><br />z-index: 1;<br /><br />}<br /><br />.l:after {<br /><br />background:<br /><br />linear-gradient(transparent 50%, rgba(0,0,0,0.15) 0) 0 50% / 50% 100%,<br /><br />repeating-linear-gradient(90deg,#bbb 0,#bbb,#bbb 20%,#999 20%,#999 40%) 0 50% / 50% 100%,<br /><br />radial-gradient(circle at 50% 50%,#888 25%, transparent 26%);<br /><br />background-repeat: no-repeat;<br /><br />border: 0.25em solid transparent;<br /><br />border-left: 0.4em solid #d8d8d8;<br /><br />border-right: 0 solid transparent;<br /><br />transition: border-left-color 0.1s 0.3s ease-out, transform 0.3s ease-out;<br /><br />transform: translateX(-22.5%);<br /><br />transform-origin: 25% 50%;<br /><br />width: 1.2em;<br /><br />height: 1em;<br /><br />}<br /><br />/* Checked */<br /><br />.l:checked {<br /><br />background-color: rgba(0,0,0,0.45);<br /><br />box-shadow: 0.125em 0.125em 0 0.125em rgba(0,0,0,0.1) inset;<br /><br />}<br /><br />.l:checked:before {<br /><br />background-color: currentColor;<br /><br />transform: translateX(125%)<br /><br />}<br /><br />.l:checked:after {<br /><br />border-left-color: currentColor;<br /><br />transform: translateX(-2.5%) rotateY(180deg);<br /><br />}<br /><br />/* Other States */<br /><br />.l:focus {<br /><br />/* Usually an anti-A11Y practice but set to remove an annoyance just for this demo */<br /><br />outline: 0;<br /><br />}<br /><br />&lt;/style&gt;<br /><br />&lt;/body&gt;<br /><br />&lt;/html&gt;[/tex<br /><br />[tex]&lt;!DOCTYPE html&gt;<br /><br />&lt;html lang="en"&gt;<br /><br />&lt;head&gt;<br /><br />&lt;title&gt;Bulb&lt;/title&gt;<br /><br />&lt;/head&gt;<br /><br />&lt;body&gt;<br /><br />&lt;main&gt;<br /><br />&lt;input class="l" type="checkbox"&gt;<br /><br />&lt;/main&gt;<br /><br />&lt;style&gt;<br /><br />*, *:before, *:after {<br /><br />box-sizing: border-box;<br /><br />margin: 0;<br /><br />padding: 0;<br /><br />}<br /><br />:root {<br /><br />/* minFontSize + (maxFontSize - minFontSize) * (100vw - minVWidth)/(maxVWidth - minVWidth) */<br /><br />font-size: calc(64px + (80 - 64) * (100vw - 320px)/(960 - 320));<br /><br />}<br /><br />body, input {<br /><br />font-size: 1em;<br /><br />line-height: 1.5;<br /><br />}<br /><br />body {<br /><br />background: #bbb;<br /><br />}<br /><br />input {<br /><br />display: block;<br /><br />margin-bottom: 1.5em;<br /><br />}<br /><br />main {<br /><br />padding: 1.5em 0 0 0;<br /><br />text-align: center;<br /><br />}<br /><br />.l {<br /><br />background-color: rgba(0,0,0,0.7);<br /><br />border-radius: 0.75em;<br /><br />box-shadow: 0.125em 0.125em 0 0.125em rgba(0,0,0,0.3) inset;<br /><br />color: #fdea7b;<br /><br />display: inline-flex;<br /><br />align-items: center;<br /><br />margin: auto;<br /><br />padding: 0.15em;<br /><br />width: 3em;<br /><br />height: 1.5em;<br /><br />transition: background-color 0.1s 0.3s ease-out, box-shadow 0.1s 0.3s ease-out;<br /><br />-webkit-appearance: none;<br /><br />-moz-appearance: none;<br /><br />appearance: none;<br /><br />}<br /><br />.l:before, .l:after {<br /><br />content: "";<br /><br />display: block;<br /><br />}<br /><br />.l:before {<br /><br />background-color: #d7d7d7;<br /><br />border-radius: 50%;<br /><br />width: 1.2em;<br /><br />height: 1.2em;<br /><br />transition: background-color 0.1s 0.3s ease-out, transform 0.3s ease-out;<br /><br />z-index: 1;<br /><br />}<br /><br />.l:after {<br /><br />background:<br /><br />linear-gradient(transparent 50%, rgba(0,0,0,0.15) 0) 0 50% / 50% 100%,<br /><br />repeating-linear-gradient(90deg,#bbb 0,#bbb,#bbb 20%,#999 20%,#999 40%) 0 50% / 50% 100%,<br /><br />radial-gradient(circle at 50% 50%,#888 25%, transparent 26%);<br /><br />background-repeat: no-repeat;<br /><br />border: 0.25em solid transparent;<br /><br />border-left: 0.4em solid #d8d8d8;<br /><br />border-right: 0 solid transparent;<br /><br />transition: border-left-color 0.1s 0.3s ease-out, transform 0.3s ease-out;<br /><br />transform: translateX(-22.5%);<br /><br />transform-origin: 25% 50%;<br /><br />width: 1.2em;<br /><br />height: 1em;<br /><br />}<br /><br />/* Checked */<br /><br />.l:checked {<br /><br />background-color: rgba(0,0,0,0.45);<br /><br />box-shadow: 0.125em 0.125em 0 0.125em rgba(0,0,0,0.1) inset;<br /><br />}<br /><br />.l:checked:before {<br /><br />background-color: currentColor;<br /><br />transform: translateX(125%)<br /><br />}<br /><br />.l:checked:after {<br /><br />border-left-color: currentColor;<br /><br />transform: translateX(-2.5%) rotateY(180deg);<br /><br />}<br /><br />/* Other States */<br /><br />.l:focus {<br /><br />/* Usually an anti-A11Y practice but set to remove an annoyance just for this demo */<br /><br />outline: 0;<br /><br />}<br /><br />&lt;/style&gt;<br /><br />&lt;/body&gt;<br /><br />&lt;/html&gt;

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