Question

what is the formula to find the value of 21C5 + 22C5 + 23C5 + . . . . .+30C5

Answer 1

see the attachment below

Answer 2

²¹C₅ + ²²C₅  + ²³C₅  + ...................................+ ²⁹C₅ + ³⁰C₅ =  ³¹C₆ - ²¹C₆

Step-by-step explanation:

²¹C₅ + ²²C₅  + ²³C₅  + ...................................+ ²⁹C₅ + ³⁰C₅

using ⁿCₓ + ⁿCₓ₋₁ = ⁿ⁺¹Cₓ

adding and subtracting ²¹C₆

= ²¹C₆ + ²¹C₅ + ²²C₅  + ²³C₅  + ...................................+ ²⁹C₅ + ³⁰C₅ - ²¹C₆

as ²¹C₆ + ²¹C₅ = ²²C₆

= ²²C₆+ ²²C₅  + ²³C₅  + ...................................+ ²⁹C₅ + ³⁰C₅ - ²¹C₆

²²C₆+ ²²C₅  = ²³C₆

=  ²³C₆ + ²³C₅  + ...................................+ ²⁹C₅ + ³⁰C₅ - ²¹C₆

and so on

= ³⁰C₆+ ³⁰C₅ - ²¹C₆

=  ³¹C₆ - ²¹C₆

²¹C₅ + ²²C₅  + ²³C₅  + ...................................+ ²⁹C₅ + ³⁰C₅ =  ³¹C₆ - ²¹C₆

Learn more:

Prove the relation rC(n r)=nC(n-1 r-1) - Brainly.in

https://brainly.in/question/14557699

If n is even and the value of nCr, is maximum, then r=​ - Brainly.in

https://brainly.in/question/13846188