Home
Class 12
MATHS
Find the sum (1xx2)/(3!)+(2xx2)^2/(4!)+(...

Find the sum `(1xx2)/(3!)+(2xx2)^2/(4!)+(3xx2)^3/(5!)+....+(20xx2)^30/(22!)`

Text Solution

Verified by Experts

The correct Answer is:
`1-(2^(21))/(22!)`
`T_(r)=(rxx2^(r ))/((r+2)!)=((r+2-2)cdot2^(r ))/((r+2)!)`
`=(2^(r ))/((r+1)!)-(2^(r+1))/((r+2)!)`
`therefore` Required sum=`sum_(r=1)^(20)[(2^(r ))/((r+1)!)-(2^(r+1))/((r+2)!)]`
`=2/(2!)-2^(21)/(22!)=1-2^(21)/(22!)`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise (Single)|93 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise (Multiple & Comprehension)|66 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.8|10 Videos

  • PROBABILITY II

    CENGAGE|Exercise JEE Advanced Previous Year|25 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

Find the sum 3/(1xx2)xx1/2+4/(2xx3)xx(1/2)^2+5/(3xx4)xx(1/2)^2+ ton terms.

Find the sum 1-1/8+1/8xx3/(16)-(1xx3xx5)/(8xx16xx24)+

Find the sum of the series 2/(1xx2)+5/(2xx3)xx2+(10)/(3xx4)xx2^2+(17)/(4xx5)xx2^3+ ton terms.

Find the sum of the series: (1)/((1xx3))+(1)/((3xx5))+(1)/((5xx7))+...+(1)/((2n-1)(2n+1))

Find the product of: (-2) xx (+50) xx (-25) xx 4