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Sum the following geometric series to infinity: 1/2+1/3^3+1/2^3+1/3^4+1/2^5+1/3^5+∞

Prove that the sum of n terms of the series: 11+103+1005+is10/9(10n−1)+n2.

Prove that : 61/2×61/4×61/8 _________ ∞=6.

Find the sum of the following series: (√2−1)+1+(√2−1)+∞

A person writes a letter to four of his friends. He asks each one of them to copy the letter and...

If S be the sum, P the product and R the sum of the reciprocals of n terms of a G.P, prove that...

Find the sum of the infinite geometric series (−5/4+5/16−5/64+...∞).

If f is a function satisfying f(x+y)=f(x)f(y) for all x,y∈N such that f(1)=3 and n∑x=1 f(x)=120...

Find the sum to n terms of the sequence (x+1/x)2,(x2+1/x2)2,(x2+1/x3)2,......

Find the sum to n terms of the sequence "an" given by an=2n+3n,nϵN.

Write the value of limx→0 sin5x / 2x

Find the equation of a line with slope -1 and cutting off an intercept of 4 units on negative.......

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