Maths-
General
Easy
Question
The correct answer is: ![left curly bracket 6 k colon k element of Z right curly bracket](data:image/png;base64,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)
Let ![A equals left curly bracket n left parenthesis n plus 1 right parenthesis left parenthesis 2 n plus 1 right parenthesis colon n element of Z right curly bracket](data:image/png;base64,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)
Putting
we get ![A equals left curly bracket horizontal ellipsis minus 30 comma negative 6 comma 0 comma 6 comma 30 comma horizontal ellipsis right curly bracket](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMAAAAAPCAYAAACyYsBmAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAwZJREFUeNrtWk9kXEEYH2tFD1WqVkRUiYrVQ/VSFVWrRFRERaiIHCJCDnvKobceeuq9qspT1WOpqKpaodaKHCJUD9FDhegph1xyWLWeFbbfyC8xHfP2TWbe/Om2P37sm53J73vffDPzzbdhrD/WmDuMEz8SOyws7hMbsCMl7hGfE68o+l4iviLugAnafOI28T2xDXs/EWsa42xtN9GN0bcdxN31vI7zxC6x7Ggif8BBodEizhGHhLZbxA1F3ybxofA8gzZfWEXgjQtBs0jc0hhrY7upbqy+nUT8ZeIycZf4hTjryIgeixtt6fkR8YWiH9/RFjzYc4P41XCsje02ujH7tm/8JRBeIr78BxfAmGKHWCdOZRzz6x5sSiyCwcb2pOAgjMW3mfE3QfyMz8PEfY0/lEcVuhEGPn/fZeSq09J3R9JRfgredujBNh40I4ZjbWy30Y3Zt8eqxjKOu6tC2zditWBx7tDtiAJfXrBrug7zuJhT5OAfcJHrYq4WTSdb03Yb3Zh9u6Na2E+Jj6W2Z8S6g4BbcBzEuieRfPeZhXNq55ik1IOdPWxG09ioSsS72FHrFgsg1bDXVNe3b8+DednXVbyojBoqAEVO6DUhzYoRFzFRIg4zjukLnlIgfnEcVbTzqspBzlgb2210Y/ZtA3F4hq0+AeyiHNphcSNVXNQeKPpNeboEN7D7mqQJNrbb6Mbs2z9sWEXJKQvvFBeXQa4C3cQRL4LXs18r+r5lfsqgdRzbMqqKHZUVaLuNbsy+7YkX0l0cTVlYyVkgRS0AOWXKey4Cm+ykDn2a3/LS2092UgKW0cIlrowj+wnGy5tFjxX/+8kQtFaE0/gO5m5SQ9/UdhtdH741jZmzNv7z9kyO80cVq9ZFGSrEAriH+0gKtvr4g1/k3qAfT+ESxcbhagFwVLBT/oL/NmG/jr6N7aa6PnxrGjPHodOMJl6kxAYPLlJGX/qhxvrSKCHumqGDpIIV3x6w4OfVke/M3f9QudQPNdanRhtxV2H/4QQ8XRz+S/VDjQ2m8RuhJE3U54pmEgAAARF0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PG1vPj08L21vPjxtbz57PC9tbz48bW8+JiN4MjAyNjs8L21vPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjMwPC9tbj48bW8+LDwvbW8+PG1vPiYjeDIyMTI7PC9tbz48bW4+NjwvbW4+PG1vPiw8L21vPjxtbj4wPC9tbj48bW8+LDwvbW8+PG1uPjY8L21uPjxtbz4sPC9tbz48bW4+MzA8L21uPjxtbz4sPC9tbz48bW8+JiN4MjAyNjs8L21vPjxtbz59PC9tbz48L21hdGg+xBH0uQAAAABJRU5ErkJggg==)
![not stretchy rightwards double arrow left curly bracket n left parenthesis n plus 1 right parenthesis left parenthesis 2 n plus 1 right parenthesis colon n element of Z right curly bracket subset of left curly bracket 6 k colon k element of Z right curly bracket](data:image/png;base64,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)
Related Questions to study
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Let
and
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denotes cartesian product of the sets A and B ; then
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denotes cartesian product of the sets A and B ; then
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If a1, a2, a3, ........., an are positive real numbers whose product is a fixed number c, then the minimum value of a1 + a2 + a3 + .... + an – 1 + 2an is
In this question, we have to find that minimum value of a1 + a2 + a3 + …… + an-1 + 2an. Remember always the inequality of A.M and G.M. Always A.M ≥ G.M.
If a1, a2, a3, ........., an are positive real numbers whose product is a fixed number c, then the minimum value of a1 + a2 + a3 + .... + an – 1 + 2an is
Maths-General
In this question, we have to find that minimum value of a1 + a2 + a3 + …… + an-1 + 2an. Remember always the inequality of A.M and G.M. Always A.M ≥ G.M.