Question

Find a value ,15 square+16 square+17 square+...+28 square

Answer 1

Answer:

maths

Step-by-step explanation:

16^2 + 17^2 + 18^2 + ... + 29^2 + 30^2 =

16^2 + 17^2 + 18^2 + ... + 29^2 + 30^2 =(1 + 15)^2 + (2 + 15)^2 + (3 + 15)^2 + ... + (14 + 15)^2 + (15 + 15)^2 =

16^2 + 17^2 + 18^2 + ... + 29^2 + 30^2 =(1 + 15)^2 + (2 + 15)^2 + (3 + 15)^2 + ... + (14 + 15)^2 + (15 + 15)^2 =(1^2 + 2*15 + 15^2) + (2^2 + 2*2*15 + 15^2) + (3^2 + 2*3*15 + 15^2) + ... + (14^2 + 2*14*15 + 15^2) + (15^2 + 2*15*15 + 15^2) =

16^2 + 17^2 + 18^2 + ... + 29^2 + 30^2 =(1 + 15)^2 + (2 + 15)^2 + (3 + 15)^2 + ... + (14 + 15)^2 + (15 + 15)^2 =(1^2 + 2*15 + 15^2) + (2^2 + 2*2*15 + 15^2) + (3^2 + 2*3*15 + 15^2) + ... + (14^2 + 2*14*15 + 15^2) + (15^2 + 2*15*15 + 15^2) =(1^2 + 2^2 + ... + 15^2) + 2*15(1 + 2 + 3 + ... + 14 + 15) + 15*15^2

16^2 + 17^2 + 18^2 + ... + 29^2 + 30^2 =(1 + 15)^2 + (2 + 15)^2 + (3 + 15)^2 + ... + (14 + 15)^2 + (15 + 15)^2 =(1^2 + 2*15 + 15^2) + (2^2 + 2*2*15 + 15^2) + (3^2 + 2*3*15 + 15^2) + ... + (14^2 + 2*14*15 + 15^2) + (15^2 + 2*15*15 + 15^2) =(1^2 + 2^2 + ... + 15^2) + 2*15(1 + 2 + 3 + ... + 14 + 15) + 15*15^2= 1240 + 3600 + 3375

16^2 + 17^2 + 18^2 + ... + 29^2 + 30^2 =(1 + 15)^2 + (2 + 15)^2 + (3 + 15)^2 + ... + (14 + 15)^2 + (15 + 15)^2 =(1^2 + 2*15 + 15^2) + (2^2 + 2*2*15 + 15^2) + (3^2 + 2*3*15 + 15^2) + ... + (14^2 + 2*14*15 + 15^2) + (15^2 + 2*15*15 + 15^2) =(1^2 + 2^2 + ... + 15^2) + 2*15(1 + 2 + 3 + ... + 14 + 15) + 15*15^2= 1240 + 3600 + 3375= 8215

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