show that the sum of n consecutive odd integers beginning with 1 equals n Square
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hope this helps uh ...
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1.
example : 121
121-1 = 120
120-3=117
117-5=112
112-7=105
105-9=96
96-11=85
85-13=72
72-15=57
57-17=40
40-19=21
21-21=0
.•. no. of steps done =11
so, 121=11^2
2.
no. of even no.s = n = 3
.•.first three even no.s = 2 , 4 , 6
sum = 12
first three odd no.s = 1 , 3 , 5
sum = 9
to prove ,
12 = (1+(1/3))*9
12=((3+1)3)*9
12=(4/3)*9
12=4*3
12=12
hence, proved
^_^
example : 121
121-1 = 120
120-3=117
117-5=112
112-7=105
105-9=96
96-11=85
85-13=72
72-15=57
57-17=40
40-19=21
21-21=0
.•. no. of steps done =11
so, 121=11^2
2.
no. of even no.s = n = 3
.•.first three even no.s = 2 , 4 , 6
sum = 12
first three odd no.s = 1 , 3 , 5
sum = 9
to prove ,
12 = (1+(1/3))*9
12=((3+1)3)*9
12=(4/3)*9
12=4*3
12=12
hence, proved
^_^
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