The value of ^2 5^ + ^2 10^ + ^2 15^ + ^2 20^ + . + ^2 90^ is

Step-by-step solution

aligned & ^2 5^ + ^2 10^ + ^2 15^ + . .+ . .+ ^2 75^ + & ^2 80^ + ^2 85^ + ^2 90^ & ^2 5^ + ^2 10^ + ^2 15^ + . . ^2 (90-15^ )+ & ^2(90-10)+ ^2(90-5)+1 & ^2 5+ ^2 10+ ^2 15^ + . .+ ^2 15^ + & ^2 10^ + ^2 5^ +1 & (1+1+1+ .8 times )+ ^2 45^ +1 & 8+ 1 2 +1= 19 2 aligned