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Prove that 1^2/(1!)+2^2/(2!)+3^2/(3!)+4^...

Prove that
`1^2/(1!)+2^2/(2!)+3^2/(3!)+4^2/(4!)+.....=2e`

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MAHAVEER PUBLICATION-SERIES-QUESTION BANK
  1. Find the sum of first n terms and the sum of first 5 terms of the geo...

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  2. Find the sum of the sequence 7, 77, 777, 7777, . . . to n terms.

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  3. How many numbers divisible by 17 are there in between 25 and 450 ?

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  4. For what value of x, the number -2/7,x ,-2/7are in G.P.?

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  5. Insert three geometric mean (GM) between 1 and 1/16.

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  6. Find three numbers in G.P. whose sum is 19 and product is 216.

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  7. If a ,b ,c are respectively the p^(t h),q^(t h)a n dr^(t h) terms of a...

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  8. Find the 12^(th) term of the sequences -6,-18,-54,…..

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  9. Find the sum of 2+4+8+16+….. to 8 terms.

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  10. 1.3+3.5+5.7+..... n terms =

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  11. Find the value of a' if (2a+1),a,(3a+2) are in G.P?

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  12. Statement -1: The sum of the series (1)/(1!)+(2)/(2!)+(3)/(3!)+(4)/(...

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  13. Prove that x/(1!)+(2x^2)/(2!)+(3x^3)/(3!)+(4x^4)/(4!)+.....=xe^x

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  14. Prove that 1^2/(1!)+2^2/(2!)+3^2/(3!)+4^2/(4!)+.....=2e

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  15. Prove that 1^3/(1!)+2^3/(2!)+3^3/(3!)+4^3/(4!)+.....=5e

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  16. Prove that 1/3+1/(3.3^3)+1/(5.3^5)+....=1/2log2

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  17. If 1-(1)/(2)+(1)/(3)-(1)/(4)+..=log(e)2, then sum (1)/(1.3)+(1)/(2.5)+...

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  18. Prove that, (1.3)/(1!)+(2.4)/(2!)+(3.5)/(3!)+(4.6)/(4!)+.....=4e

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  19. Show that, 1/(1-x)=1+x+x^2+x^3+....infty if |x|lt1

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  20. ((1 )/(2!) + (1)/(4!) + (1)/(6!) + ......)/((1)/(1!) + (1)/(3!) + (1)/...

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