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Sum of the following series (i) 1+(2)/...

Sum of the following series
(i) `1+(2)/(2)+(3)/(2^2)+(4)/(2^3)+`……..to n terms
(ii) `1+(3)/(4)+(7)/(16)+(15)/(64)+(31)/(256)+……….` to infinity.

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(i) `4-(2+n)/(2^(n-1))`,
(ii) `8//3`.
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MOTION-SEQUENCE & SERIES -Exercise -3 Subjective /JEE Advanced
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  2. The sum of infinite number of terms of a G.P. is 4 and the sum of thei...

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  3. Sum of the following series (i) 1+(2)/(2)+(3)/(2^2)+(4)/(2^3)+……..to...

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  4. The sum of first ten terms of an A.P. is 155 and the sum of first two ...

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  5. In a set of four number, the first three are in GP & the last three ar...

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  7. Find the sum of the n terms of the series whose nth term is (i) n(n+...

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  9. If the expression exp {1+|cosx|+cos^(3)x|+cos^(4)x+ . . . . oo)log(e...

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  11. Find the sum of the n terms of the sequence 1/(1+1^2+1^4)+2/(1+2^2+2^...

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  12. Find the sum of the first n terms ofthe sequence : 1+2(1+1/n)+3(1+1/n)...

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  13. Find the n term and the sum to n terms of the sequence: (i) 1+5+13+29+...

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  14. If sqrt(1+1/(1^2)+1/(2^2))+sqrt(1+1/(2^2)+1/(3^2))+sqrt(1+1/(3^2)+1/(4...

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  15. If a1,a,a3...an are in A.P then prove that a1^2-a2^2+a3^2-a4^2+....a(2...

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  16. If a, b, c, d, e be 5 numbers such that a, b, c are in AP, b, c, d, ar...

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  18. Prove that b^2c^2+c^2a^2+a^2b^2gtabc(a+b+c), where a,b,c gt 0 .

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  19. The arithmetic mean of two numbers is 6 and their geometric mean G and...

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