Home
Class 12
MATHS
Sum the following infinite series (p-q...

Sum the following infinite series `(p-q) (p+q) + (1)/(2!) (p-q)(p+q) (p^(2) + q^(2))+(1)/(3!) (p-q) (p+q) (p^(4)+q^(4)+p^(2) q^(2)) + ...oo`

Text Solution

Verified by Experts

The given series can be rewritten as
` (p^(2)- q^(2)) + (1)/(2!)(p^(4) -q^(4)) + (1)/(3!) (p^(6) -q^(6))+ ...oo`
`( p^(2) + (1)/(2!) p^(4) + (1)/(3!) p^(6) + ...oo) - (q^(2) + (1)/(2!) q^(4) + (1)/(3!)q^(6) +...oo)`
` = (e^(p^(2))-1) -(e^(q^(3))-1) = e^(p^(2)) - e^(q^(2))`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    AAKASH INSTITUTE|Exercise Try Yourself|85 Videos

  • SEQUENCES AND SERIES

    AAKASH INSTITUTE|Exercise Assignment (SECTION - A) One option is correct|60 Videos

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment (Section - J) Aakash Challengers Questions|8 Videos

  • SETS

    AAKASH INSTITUTE|Exercise SECTION-I(Aakash Challengers Questions)|5 Videos

Similar Questions

Explore conceptually related problems

Factorise p ^(4) + q ^(4) + p ^(2) q ^(2).

p-2q-p^(2)+4q^(2)

Solve the following system of equations.(x)/(p)+(y)/(q)=1p(x-p)-q(y+q)=2p^(2)+q^(2)

Solve the following system of equations.(x)/(p)+(y)/(q)=1p(x-p)-q(y+q)=2p^(2)+q^(2)

Simplified form of (p+(1)/(q))^((p-q))(p-(1)/(q))^((p+q))(q+(1)/(p))^((p-q))(q-(1)/(p))^((p+q))

Add the following expressions: p^2-q +r, q^2 -r+ p and r^2-p+q