find the value of 2^1/4.2^1/5
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2^1/4×2^2/8×2^3/16×2^4/32×2^5/64………infinite.
P=(2)^(1/4+2/8+3/16+4/32+5/64+……….infinite).
P=(2)^S…………………..(1)
Where S=1/4+2/8+3/16+4/32+5/64+…………infinite………..(2).
S ×(1/2) = 1/8+2/16+3/32+4/64+…………….…………………..infinite…….(3).
On subtracting eq.(3) from (2).
S/2=1/4+1/8+1/16+1/32+1/64+………. infinite.
S/2=a/(1-r) = (1/4)/(1–1/2).
S/2 =1/4×2/1.
S/2 = 1/2
S = 1.
put S=1 in eq.(1).
P =(2)^S.
P =(2)^1
P = 2 . Answer.
Step-by-step explanation:
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